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t spending g or increasing the net of exports minus imports x m the classical microeconomics of labour markets economists see the labour market as similar to any other market in that the forces of supply and demand jointly determine price in this case the wage rate and quantity in this case the number of people employed however the labour market differs from other markets like the markets for goods or the money market in several ways perhaps the most important of these differences is the function of supply and demand in setting price and quantity in markets for goods if the price is high there is a tendency in the long run for more goods to be produced until the demand is satisfied with labour overall supply cannot effectively be manufactured because people have a limited amount of time in the day and people are not manufactured a rise in overall wages will in many situations not result in more supply of labour it may result in less supply of labour as workers take more time off to spend their increased wages |
or it may result in no change in supply within the overall labour market particular segments are thought to be subject to more normal rules of supply and demand as workers are likely to change job types in response to differing wage rates many economists have thought that in the absence of laws or organizations such as unions or large multinational corporations labour markets can be close to perfectly competitive in the economic sense that is there are many workers and employers both having perfect information about each other and there are no transaction costs the competitive assumption leads to clear conclusions workers earn their marginal product of labour other economists focus on deviations from perfectly competitive labour markets these include job search training and gaining of experience costs to switch between job types efficiency wage models and oligopsony monopsonistic competition neoclassical microeconomic model supply households are suppliers of labour in microeconomics theory people are assumed |
rational and seeking to maximize their utility function in this labour market model their utility function is determined by the choice between income and leisure however they are constrained by the waking hours available to them let w denote hourly wage let k denote total waking hours let l denote working hours let denote other incomes or benefits let a denote leisure hours the utility function and budget constraint can be expressed as following max u w l a such that l a k this can be shown in a diagram below that illustrates the trade off between allocating your time between leisure activities and income generating activities the linear constraint line indicates that there are only two four hours in a day and individuals must choose how much of this time to allocate to leisure activities and how much to working if multiple days are being considered the maximum number of hours that could be allocated towards leisure or work is about one six everyone has to sleep eventually this allocation decision is informe |
d by the curved indifference curve labelled ic the curve indicates the combinations of leisure and work that will give the individual a specific level of utility the point where the highest indifference curve is just tangent to the constraint line point a illustrates the short run equilibrium for this supplier of labour services income leisure trade off in the short run the income leisure trade off in the short run if the preference for consumption is measured by the value of income obtained rather than work hours this diagram can be used to show a variety of interesting effects this is because the slope of the budget constraint becomes the wage rate the point of optimization point a reflects the equivalency between the wage rate and the marginal rate of substitution leisure for income the slope of the indifference curve because the marginal rate of substitution leisure for income is also the ratio of the marginal utility of leisure mul to the marginal utility of income muy one can conclude over over effects |
of a wage increase effects of a wage increase if wages increase this individual s constraint line pivots up from x y one to x y two he she can now purchase more goods and services his her utility will increase from point a on ic one to point b on ic two to understand what effect this might have on the decision of how many hours to work you must look at the income effect and substitution effect the wage increase shown in the previous diagram can be decompiled into two separate effects the pure income effect is shown as the movement from point a to point c in the next diagram consumption increases from ya to yc and assuming leisure is a normal good leisure time increases from xa to xc employment time decreases by the same amount xa to xc the income and substitution effects of a wage increase the income and substitution effects of a wage increase but that is only part of the picture as the wage rate rises the worker will substitute work hours for leisure hours that is will work more hours to take advantage of th |
e higher wage rate or in other words substitute away from leisure because of its higher opportunity cost this substitution effect is represented by the shift from point c to point b the net impact of these two effects is shown by the shift from point a to point b the relative magnitude of the two effects depends on the circumstances in some cases the substitution effect is greater than the income effect in which case more time will be allocated to working but in other cases the income effect will be greater than the substitution effect in which case less time is allocated to working the intuition behind this latter case is that the worker has reached the point where his marginal utility of leisure outweighs his marginal utility of income to put it in less formal and less accurate terms there is no point in earning more money if you don t have the time to spend it the labour supply curve the labour supply curve if the substitution effect is greater than the income effect the supply of labour curve diagram to t |
he left will slope upwards to the right as it does at point e for example this individual will continue to increase his supply of labour services as the wage rate increases up to point f where he is working hf hours each period of time beyond this point he will start to reduce the amount of labour hours he supplies for example at point g he has reduced his work hours to hg where the supply curve is sloping upwards to the right positive wage elasticity of labour supply the substitution effect is greater than the income effect where it slopes upwards to the left negative elasticity the income effect is greater than the substitution effect the direction of slope may change more than once for some individuals and the labour supply curve is likely to be different for different individuals other variables that affect this decision include taxation welfare and work environment neoclassical microeconomic model demand this article has examined the labour supply curve which illustrates at every wage rate the maximum qu |
antity of hours a worker will be willing to supply to the economy per period of time economists also need to know the maximum quantity of hours an employer will demand at every wage rate to understand the quantity of hours demanded per period of time it is necessary to look at product production that is labour demand is a derived demand it is derived from the output levels in the goods market a firm s labour demand is based on its marginal physical product of labour mpl this is defined as the additional output or physical product that results from an increase of one unit of labour or from an infinitesimally small increase in labour if you are not familiar with these concepts you might want to look at production theory basics before continuing with this article the marginal physical product of labour the marginal physical product of labour in most industries and over the relevant range of outputs the marginal physical product of labour is declining that is as more and more units of labour are employed their ad |
ditional output begins to decline this is reflected by the slope of the mppl curve in the diagram to the right if the marginal physical product of labour is multiplied by the value of the output that it produces we obtain the value of marginal physical product of labour mppl pq vmppl the value of marginal physical product of labour vmppl is the value of the additional output produced by an additional unit of labour this is illustrated in the diagram by the vmppl curve that is above the mppl in competitive industries the vmppl is in identity with the marginal revenue product of labour mrpl this is because in competitive markets price is equal to marginal revenue and marginal revenue product is defined as the marginal physical product times the marginal revenue from the output mrp mpp mr a firm s labour demand in the short run a firm s labour demand in the short run the marginal revenue product of labour can be used as the demand for labour curve for this firm in the short run in competitive markets a firm face |
s a perfectly elastic supply of labour which corresponds with the wage rate and the marginal resource cost of labour w sl mfcl in imperfect markets the diagram would have to be adjusted because mfcl would then be equal to the wage rate divided by marginal costs because optimum resource allocation requires that marginal factor costs equal marginal revenue product this firm would demand l units of labour as shown in the diagram neoclassical microeconomic model equilibrium the demand for labour of this firm can be summed with the demand for labour of all other firms in the economy to obtain the aggregate demand for labour likewise the supply curves of all the individual workers mentioned above can be summed to obtain the aggregate supply of labour these supply and demand curves can be analysed in the same way as any other industry demand and supply curves to determine equilibrium wage and employment levels information approaches since the one nine seven zero s some attention has shifted to the information charac |
teristics of the labour market in the classical model it is assumed that both sides know how much work effort and marginal product the employee contributes in many real life situations this is far from the case the firm does not necessarily know how hard a worker is working or how productive they are this provides an incentive for workers to shirk from providing their full effort since it is difficult for the employer to identify the hard working and the shirking employees there is no incentive to work hard and productivity falls overall the methods used to overcome this type of problem have been studied by modern labour economists one solution used recently stock options grants employees the chance to benefit directly from the firm s success however this solution has attracted criticism as executives with large stock option packages have been suspected of acting to over inflate share values to the detriment of the long run welfare of the firm search models one of the major research achievements of the last t |
wo zero years has been the development of a framework with dynamic search match and bargaining work started in the early one nine eight zero s with contributions from peter diamond dale t mortensen and others which characterized equilibrium in such model economies later this framework was tailored to the labour market more recently mortensen and christopher a pissarides have extended the framework to include labour market institutions such as unemployment insurance and employment protection criticisms of labour economics one critique of standard economic analysis of labour markets is that it does not account for the importance of social networks in the employment process this view holds that personal connections are key for both workers and employees hence employees are more likely to apply for jobs where they have a personal connection and are more likely to be hired if they apply more generally sociologists and political economists claim that labour economics tends to lose sight of the complexity of individ |
ual employment decisions these decisions particularly on the supply side are often loaded with considerable emotional baggage and a purely numerical analysis can miss important dimensions of the process also missing from most labour market analysis is the role of unpaid labour even though this type of labour is unpaid it can nevertheless play an important part in society the most dramatic example is child raising unpaid work is typically ignored because it is difficult to measure and there is no agreed upon method of incorporating it into standard analysis when the unpaid labour variable is ignored the model s conclusions might be biased see also unemployment beveridge curve consumer theory production theory basics microeconomics important publications in labour economics labour power external links richard freeman labor worklife program at harvard law school changing labor markets project labor in english speaking countries august one is lammas day loaf mass day the festival of the first wheat harvest of the |
year on this day it was customary to bring to church a loaf made from the new crop in many parts of england tenants were bound to present freshly harvested wheat to their landlords on or before the first day of august in the anglo saxon chronicle where it is referred to regularly it is called the feast of first fruits the blessing of new fruits was performed annually in both the eastern and western churches on the first or the sixth of august the sacramentary of pope gregory i d six zero four specifies the sixth in medieval times the feast was known as the gule of august but the meaning of gule is unknown ronald hutton suggests that it may be an anglicisation of gwyl aust the welsh name for august one meaning feast of august but this is not certain if so this points to a pre christian origin for lammas among the anglo saxons and a link to the gaelic festival of lughnasadh in modern neo paganism the name lammas is used for one of the sabbats taking place on august one this festival is also known as lughnasadh |
lammas is one of the scottish quarter days lammas is also a finnish word and means sheep see also harvest festival harvest home ould lammas fair references the stations of the sun ronald hutton oxford one nine nine six romeo and juliet william shakespeare not specified christian festivals the long meddowe days festival is held on the town green each may vendors sell antiques and local curiosities longmeadow is a town in hampden county massachusetts as of the two zero zero zero census the town had a total population of one five six three three its town government consists of a board of selectmen with three members history longmeadow was first settled in one six four four and officially incorporated in one seven eight three the town was originally farmland within the limits of springfield it remained relatively pastoral until the end of world war ii when the population tripled over a fifteen year period today it is perhaps the most affluent suburb in the pioneer valley region between springfield and hartford j |
ohnny appleseed once lived there as did celebrities like actress bridget moynahan and total request live host damien fahey geography image longmeadow ma highlight png longmeadow is located in the western part of the state just south of the city of springfield and is bordered on the west by the connecticut river and to the south by enfield connecticut it extends approximately three miles north to south and two five miles east to west it is approximately two zero miles north of hartford longmeadow has a town common located along us highway five on the west side of town it is about zero seven five miles one two kilometers long the town has three elementary schools two secondary schools and one high school the commercial center of town is an area called the shops including restaurants and clothing stores according to the united states census bureau the town has a total area of two four six km nine five mi two three four km nine zero mi of it is land and one two km zero five mi of it is water the total area is fiv |
e zero five water demographics as of the census of two zero zero zero there are one five six three three people five seven three four households and four four three two families residing in the town the population density is six six nine two km one seven three two five mi there are five eight seven nine housing units at an average density of two five one seven km six five one five mi the racial makeup of the town is nine five four two white zero six nine african american zero zero five native american two nine zero asian zero zero six pacific islander zero two six from other races and zero six two from two or more races one zero nine of the population are hispanic or latino of any race there are five seven three four households out of which three seven one have children under the age of one eight living with them six nine one are married couples living together six four have a female householder with no husband present and two two seven are non families two zero four of all households are made up of individua |
ls and one four zero have someone living alone who is six five years of age or older the average household size is two six six and the average family size is three zero nine in the town the population is spread out with two six eight under the age of one eight four six from one eight to two four two two zero from two five to four four two eight seven from four five to six four and one seven eight who are six five years of age or older the median age is four three years for every one zero zero females there are eight seven seven males for every one zero zero females age one eight and over there are eight two zero males the median income for a household in the town is seven five four six one and the median income for a family is eight seven seven four two males have a median income of eight eight two three eight versus four zero eight nine zero for females the per capita income for the town is three eight nine four nine two one of the population and one zero of families are below the poverty line out of the tot |
al population zero three of those under the age of one eight and eight three of those six five and older are living below the poverty line external links towns in massachusetts hampden county massachusetts a right handed cartesian coordinate system illustrating the x right left y forward backward and z up down axes relative to a human being in this illustration right up and forward are positive vectors while left down and backward are negative vectors left and right are defined from the boxer s perspective rather than the viewer s the most common relative directions are left right forward backward up and down there is no universal direction which can be said to be either one of them scientifically this is expressed as that there is no absolute inertial frame of reference one famed attempt to discern what is the real up and down in the universe was the michelson morley experiment the fame comes from the experiment s complete failure something which eventually led up to the albert einstein s theories of relativ |
ity these conclude that it is not possible to find an absolute up or down the upshot of this is that the most basic concepts of direction known to mankind cannot be scientifically defined they are in effect defined through tradition and word of mouth this also means that in order to use these directions to express oneself one first has to define a reference the easiest relative directions to define are up and down the most common definition uses gravity and the planet earth as a frame of reference since there is a very noticable force of gravity acting between the earth and any other object down is defined as that direction which an object moves in reference to the earth when the object is left to fall freely up is then defined as the opposite direction of down another common definition uses a human body standing upright as a frame of reference in that case up is defined as the direction from feet to head peripendicular to the surface of the earth forward and backward are most commonly defined by refering to |
an object or person s motion forward is defined as the direction in which the object is moving backwards is then defined as the opposite of forward the terms left and right are derived from the fact that some nine zero of the population use the hand of the same side of their body for writing and other manual tasks through cognate of the word right in the meaning correct or good the side with the hand most used was defined as the right side the word left comes from the old english lyft meaning weak this dichotomy can also be seen in the words dextrous and sinister from the latin words for right and left in the vast majority of the population the heart is slightly to the left of the body s centre line and the liver is to the right less visibly the two hemispheres of the brain differ in function in nautical usage the halves of a ship are designated port left and starboard right relative to a person looking forward towards the bow of the ship in politics left and right are labels applied to parts of a theoretical |
spectrum of opinion left is associated with socialism and in the united states with liberalism and the democratic party in the extreme left can be associated with communism and anarchism right is associated with conservatism and in the united states with the republican party elsewhere in the world it is also often associated with liberalism in the extreme right can be associated with fascism this usage derives from the seating of parliamentary partisans during the french revolution see left right politics example see text for explanation in this diagram showing a road with rules of the road hand traffic the red car is to the left of the blue car the blue car is therefore on the right hand side should the blue car move back ward it would reach the position of the yellow car for the red car to be where the green car is it would have to move forward the lane containing the green and red cars is the left lane the lane with the yellow and blue cars is the right lane orientation lizards are reptiles of the order s |
quamata which they share with the snakes ophidians they are usually four legged with external ear openings and movable eyelids species range in adult length from a few centimeters some caribbean geckos to nearly three meters komodo dragons some lizard species called glass snakes or glass lizards have no functional legs though there are some vestigial skeletal leg structures they are distinguished from true snakes by the presence of eyelids and ears many lizards can change color in response to their environments or in times of stress the most familiar example is the chameleon but more subtle color changes occur in other lizard species as well most notably the anole also known as the house chameleon or chamele lizards typically feed on insects or rodents a few species are omnivorous or herbivorous a familiar example of the latter is the iguana which is unable to properly digest animal protein until very recently it was thought that only two lizard species were venomous the mexican beaded lizard and the closely |
related gila monster both of which live in northern mexico and the southwest united states however recent research at the university of melbourne australia and pennsylvania state university has revealed that in fact many lizards in the iguanians and monitor lizard families have venom producing glands none of these poses much danger to humans as their poison is introduced slowly by chewing rather than injected as with poisonous snakes nine toxins previously thought to only occur in snakes have been discovered and a number of previously unseen chemicals as well these revelations are prompting calls for a complete overhaul of the classification system for lizard species to form a venom clade these papers threaten to radically change our concepts of lizard and snake evolution and particularly of venom evolution says harry greene a herpetologist at cornell university in new york most other lizard species are utterly harmless to humans most species native to north america for example are incapable even of drawing b |
lood with their bites only the very largest lizard species pose any threat at all the komodo dragon for example has been known to attack and kill humans and their livestock the chief impact of lizards on humans is positive they are significant predators of pest species numerous species are prominent in the pet trade some are eaten as food for example iguanas in central america and lizard symbology plays important though rarely predominant roles in some cultures e g tarrotarro in australian mythology most lizards lay eggs though a few species are capable of live birth many are also capable of regeneration of lost limbs or tails lizards in the scincomorpha family which include skinks such as the blue tailed skink often have shiny iridescent scales that appear moist however like all other lizards they are dry skinned and generally prefer to avoid water though all lizards are able to swim if needed classification coachella valley fringe toed lizard uma inornata plumed basilisk basiliscus plumifrons zebra tailed l |
izard callisaurus draconoides suborder sauria lacertilia lizards infraorder iguania family agamidae agamas family chamaeleonidae chameleons family corytophanidae casquehead lizards family crotaphytidae collared and leopard lizards family hoplocercidae wood lizards clubtails family iguanidae iguanas and spinytail iguanas family leiocephalidae see tropidurinae family leiosauridae see polychrotinae family liolaemidae see tropidurinae family opluridae madagascar iguanids family phrynosomatidae earless spiny tree side blotched and horned lizards family polychrotidae anoles family tropiduridae neotropical ground lizards infraorder gekkota family gekkonidae geckos family pygopodidae legless lizards family dibamidae blind lizards infraorder scincomorpha family scincidae skinks family lacertidae wall lizards or true lizards family teiidae tegus and whiptails family cordylidae spinytail lizards family gerrhosauridae plated lizards family gymnophthalmidae spectacled lizards family xantusiidae night lizards infraorder di |
ploglossa family anguidae glass lizards family anniellidae american legless lizards family xenosauridae knob scaled lizards infraorder platynota varanoidea family varanidae monitor lizards family lanthanotidae earless monitor lizards family helodermatidae gila monsters family mosasauridae marine lizards references anthony herrel s lizard page the embl reptile database tiny gecko the world s smallest lizard venom found to be widespread in lizards scaled reptiles lizards pet reptiles this is a partial list of believers in deism the belief in a god based on natural religion only or belief in religious truths discovered by people through a process of reasoning independent of any revelation through scripture or prophets they have been selected for their influence on deism or for their fame in other areas ethan allen aristotle henry st john one st viscount bolingbroke napoleon bonaparte cicero paul davies albert einstein antony flew benjamin franklin frederick the great johann wolfgang von goethe stephen hawking ed |
ward herbert one st baron herbert of cherbury william hogarth david hume hume s religious views are very ambiguous as he lived in a time when explicit opposition to church doctrine could mean death most attempts to analyze his spiritual views are based on his philosophical dialogs and experts are split on whether he was an atheist or a deist based on these see also list of atheists thomas jefferson immanuel kant gotthold ephraim lessing abraham lincoln john locke james madison bill maher moses mendelssohn gouverneur morris thomas paine elihu palmer plato alexander pope maximilien robespierre baruch spinoza lysander spooner alfred lord tennyson matthew tindal john toland constantin fran ois de chasseb uf comte de volney voltaire george washington though washington s religious beliefs are a matter of dispute there is considerable evidence that indicates that washington like numerous other men of his time was a deist believing in god but not in revelation or miracles rev dr james abercrombie the rector of washin |
gton s church responded to an inquiry about washington s beliefs after his death by saying sir washington was a deist however several of washington s family members have said that he was christian although he did not go to episcopal church on communion sundays and refused an opportunity to meet with a clergyman while on his deathbed alan watts keith r wright see also list of people by belief external links ponder list of famous deists world union of deists deism lists of people by belief this is an incomplete list which can or may never satisfy any subjective standard for completeness revisions and additions are welcome a list of prominent and famous people who are hindus religious figures philosophers adi shankara philosopher saint social reformer abhinavagupta exponent of kashmir saivism agastyar saint first and foremost person of siddha aksapada gautama author of nyaya sutras the foundation of the nyaya school of hinduism annie besant theosophist and president of the congress party sri aurobindo mystic and |
philosopher auvaiyar beloved tamil female saint a c bhaktivedanta swami prabhupada founder acharya of iskcon bhakti vaibhava puri maharaj founder acharya of the sri krishna chaitanya mission bharata advocated advaita philosophy bharat the other name for india is named after him bhartrihari author of vairagya satakam hundred verses of renunciation bhaskara raya author of varivasya rahasyam bogar legendary south indian siddhar created lord murugan statue in palani krishna chandra bhattacharya philosopher kanakadasa saint of bhakti movement swami chinmayananda religious leader deepak chopra personality development author ananda coomaraswamy art historian dattatreya narrated jnana kanda taught ashtanga yoga to patanjali swami dayananda religious leader shri madhvacharya philosopher saint frank gaetano morales philosopher hindu reconstructionist dharma teacher narayana guru mystic and philosopher nisargadatta maharaj teacher patanjali founder of patanjali yoga ram dass american spiritual leader ramana maharshi my |
stic ram mohan roy reformer sri ramakrishna paramhansa philosopher saint social reformer ramanuja philosopher saint sarvepalli radhakrishnan vedantic philosopher shankaracharya of kanchi hindu seer one seven seven five ruler of gurkha from one seven four three pratap singh shah one seven seven five one seven seven seven rana bahadur shah one seven seven seven one seven nine nine girvan yudha bikram shah one seven nine nine one eight one six rajendra bikram shah one eight one six one eight four seven surendra bikram shah one eight four seven one eight eight one prithvi bir bikram shah one eight eight one one nine one one tribhuvan bir bikram shah one nine one one one nine five five first time mahendra bir bikram shah one nine five six one nine seven two birendra bir bikram shah dev one nine seven two two zero zero one dipendra bir bikram shah dev two zero zero one gyanendra bir bikram shah dev two zero zero one present second time cambodia jayavarman i seven th century suryavarman i one zero zero two one zero |
five zero udayadityavarman ii one zero five zero one zero six six suryavarman ii one one one three one one five zero dharanindravarman ii one one five zero one one six zero indonesia gajah mada prime minister of majapahit one four th century hayam wuruk ruler of majapahit one four th century sabdapalon priest advisor to king of majapahit one five th century jayabaya ruler of kediri one two th century airlangga ruler of kediri two zero th century mohandas gandhi national leader cn annadurai popularly known as anna ex chief minister balgangadhar tilak national leader bidhan chandra roy indian politician dayanidhi maran politician it finance minister of india s dhanabalan ex minister various portfolios singapore s jayakumar deputy prime minister singapore j jayalalithaa chief minister of tamil nadu yesteryears actress m karunanidhi ex chief minister t t krishnamachari industrialist oil minister of india murasoli maran politician ex industries minister of india velupillai prabhakaran chief of the ltte c rajagopal |
achari ex governor general of india writer yesteryears actor ramaswamy venkataraman ex president india s r nathan president singapore e m s namboothiripad communist leader samy vellu works minister malaysia sarvepalli radhakrishnan ex president india chidambaram subramaniam ex steel bharat ratna awardee desh deshpande founder of sycamore networks indra nooyi president pepsico rajat gupta ceo mckinsey sanjay kumar ceo computer associates international sanjiv ahuja ceo orange telecommunications sanjiv sidhu founder i two technologies srichanda hinduja hinduja brothers vinod khosla venture capitalist co founder sun microsystems writers poets ancient times to one nine th century aathreya telugu poet auvaiyar saivite saint and tamil poet bharathidasan tamil poet interpreter of maladies kalhana kamala markandaya poetess kannadasan tamil poet ek racha patal ki hindi well known poet shashi tharoor author of the great indian novel besides other books subhash kak writer sumitranandan pant hindi poet vikram seth english |
novelist poet vayalar ramavarma malayalam poet savitri devi mukherji writer and devotee of adolf hitler scientists inventors ancient times to one nine th century madhav eight th century a d medical text author and systematizer charaka indian physician one of the founders of ayurveda susruta indian surgeon one of the earliest to perform plastic surgery two zero th century amartya sen economist nobel prize winner abhay ashtekar loop quantum gravity researcher sabeer bhatia co founder of hotmail sir chandrasekhara venkata raman one nine three zero nobel prize winner in physics r chidambaram scientific adviser to prime minister ex chairman of atomic energy commission ganapathi thanikaimoni palynologist french institute of pondicherry awarded the fyson prize in natural science har gobind khorana scientist nobel prize winner jagdish chandra bose scientist developer of wireless communication marti subrahmanyam finance expert professor at nyu university of michigan business school v s ramachandran neuroscientist dir |
ector professor at uc san diego s s ratnam pioneer in singapore in vitro fertilisation s r ranganathan eminent librarian who devised the five laws of library science srinivasa aiyangar ramanujan brilliant two zero th century mathematician subrahmanyan chandrasekhar one nine eight three nobel prize winner in physics chandrasekhara raman one nine three zero nobel prize in physics mathematicians yajnavalkya one eight zero zero bc the author of the altar mathematics of the shatapatha brahmana lagadha author of a one three five zero bc text on vedic astronomy baudhayana eight zero zero bc manava seven five zero bc apastamba seven zero zero bc aksapada gautama five five zero bc logician katyayana four zero zero bc panini five th century bc pingala five th century bc bharata muni four five zero bc aryabhata astronomer who gave very accurate calculations for astronomical constants five zero zero varahamihira bhaskara i six two zero brahmagupta helped bring the concept of zero into arithmetic virahanka eight th centur |
y gave explicit rules for the fibonacci series shridhara between six five zero eight five zero gave a good rule for finding the volume of a sphere lalla seven two zero seven nine zero govindsvamin nine th century virasena mahavira nine th century jayadeva nine th century prithudaka nine th century halayudha one zero th century aryabhata ii nine two zero one zero zero zero vateshvara one zero th century brahmadeva one zero six zero one one three zero sripati one zero one nine one zero six six gopala studied fibonacci numbers before fibonacci hemachandra also studied fibonacci numbers before fibonacci bhaskara conceived of differential calculus gangesha upadhyaya one three th century logician mithila school pakshadhara sone of gangehsa logician mithila school shankara mishra logician mithila school narayana pandit madhava considered the father of mathematical analysis founded some concepts of calculus parameshvara one three six zero one four five five nilakantha somayaji mathematician and astronomer mahendra su |
ri one four th century shankara variyar c one five three zero vasudeva sarvabhauma one four five zero one five two five logician navadvipa school raghunatha shiromani one four seven five one five five zero logician navadvipa school mathuranatha tarkavagisha c one five seven five logician navadvipa school jyesthadeva jagadisha tarkalankara c one six two five logician navadvipa school gadadhara bhattacharya c one six five zero logician navadvipa school munishvara one seven th century kamalakara one six five seven jagannatha one seven three zero jagdish chandra bose one eight five eight one nine three seven srinivasa ramanujan one eight eight seven one nine two zero a a krishnaswami ayyangar one eight nine two one nine five three meghnad saha one eight nine three one nine five six prasanta chandra mahalanobis one eight nine three one nine seven two satyendra nath bose one eight nine four one nine seven four mathematical physicist famous for bose einstein statistics raj chandra bose one nine zero one one nine eig |
ht seven d k ray chaudhuri harish chandra one nine two three one nine eight three c radhakrishna rao gopalasamudram narayana iyer ramachandran one nine two two two zero zero one shreeram shankar abhyankar one nine three zero shakuntala devi one nine three nine vijay kumar patodi one nine four five one nine seven six narendra karmarkar one nine five seven m v subbarao kanya manoj bharatanatyam dancer based in atlanta usa musicians singers dancers ravi shankar sitar virtuoso multiple grammy winner mentor to george harrison george harrison musician and member of the beatles boy george musician and member of culture club abhijeet singer alka yagnik singer asha bhosle singer babul supriyo balamurali krishna geeta dutt singer hemant kumar composer and singer hridaynath mangeshkar composer ilayaraja famous tamil film songs composer kannadasan famous tamil film songs lyricist kanya manoj bharatanatyam dancer based in atlanta usa kartik seshadri sitarist kavita krishnamurthy kay kay singer kishore kumar playback singe |
r actor lata mangeshkar singer mahendra kapoor singer manna dey singer medha hari bharatanatyam dancer ms subbulakshmi classical carnatic singer mukesh singer nitin sawhney composer o p nayyar composer rahul dev burman composer ravi composer s d burman composer sadhana sargam salil chowdhury composer suraiya singer trilok gurtu percussionist yesudas singer devotional and film songs exponent of carnatic music film producers directors satyajit ray film director adoor gopalakrishnan bimal roy boney kapoor david dhawan dev anand gemini ganesan guru dutt hrishikesh mukherjee k c bokadia kamal amrohi karan johar mani ratnam manoj night shyamalan born indian later american citizen mira nair mrinal sen raj kapoor rajkumar santoshi ram gopal varma ritwik ghatak sai paranjpe satish kaushik shekhar kapoor shyam benegal subhash ghai subodh mukherjee shakti samanta vishal bharadwaj yash chopra actors actresses abhishek bachchan abhay deol dhramendra s nephew aftab shivdasani amrish puri amitabh bachchan ajay devgan akshay |
khanna akshay kumar amol palekar anil kapoor annu kapoor aman verma anupam kher ashok kumar asha parekh aishwarya rai balraj sahni bobby deol dharmendara s son and sunny s younger brother dev anand dharmendra born one nine three five govinda gulshan grover guru dutt hrithik roshan jackie shroff jeetendra juhi chawla kamal haasan karan kapoor shashi kapoor s son koena mitra madhavan mark zuber manoj bajpai manoj kumar mithun chakraborty mohanlal navin nischol om prakash om puri padma lakshmi prabhu pran rajini kanth raj kapoor actor and director rajendra kumar raaj kumar hindi actor rajeev kapoor rajesh khanna dr rajkumar kannada actor rakesh roshan randhir kapoor rishi kapoor roshan seth sanjay dutt sanjay kapoor sanjeev kumar shahid kapoor shakti kapoor shammi kapoor shashi kapoor shatish kaushik shatrughan sinha sivaji ganesan sunil dutt sunil shetty sunny deol suresh gopi tusshar kapoor utpal dutt uttam kumar vinod khanna vinod mehra vivek oberoi sports figures golf vijay singh golf jyoti randhawa golf ar |
jun atwal golf chess viswanathan anand chess p harikrishna chess krishnan sasikiran chess murugan thiruchelvam chess pravin thipsay chess ramachandran ramesh chess tennis mahesh bhupathi tennis ramesh krishnan tennis karan rastogi tennis formula one racing narain karthikeyan formula one racing cricket anil kumble cricket chandu borde cricket javagal srinath cricket kapil dev cricket lakshmipathy balaji cricket mohinder amarnath cricket rahul dravid cricket sachin tendulkar cricket saurav ganguly cricket sunil gavaskar cricket dilip vengsarkar cricket bhagwat chandrasekhar cricket rohan kanhai cricket raman subba row cricket vinoo mankad cricket lala amarnath cricket vijay merchant cricket ck nayudu cricket maharajkumar of vizianagram cricket kumar shri ranjitsinhji cricket ranji trophy named in his honour kumar shri duleepsinhji cricket duleep trophy named in his honour muttiah muralitharan cricket fast bowler for sri lanka v v s laxman cricket shivnarine chanderpaul cricket west indies captain ramnaresh sarw |
an cricket west indies mahendra nagamootoo cricket west indies ice hockey manny malhotra hockey ashok kumar hockey baljeet singh dhillon hockey dhanraj pillay hockey dhyan chand hockey tirkey hockey badminton prakash padukone badminton gopichand badminton other sports geet sethi snooker p t usha athlete asian games medallist karnam malleswari weightlifting baichung bhutia football activists vandana shiva noted environmentalist critic of globalisation medha patkar noted environmentalist opponent of narmada dam hindu proletariat gautam tripathi a hindu others chotta rajan underworld kingpin who picked up fight with international muslim terrorist and underworld don dawood ibrahim kalpana chawla astronaut varadharajan mudaliar known as vardha bhai former prominent underworld kingpin the tamil film nayagan and hindi film nayakan starring vinod khanna madhuri dikshit feroz khan and tinoo anand are based on his life veerappan sandalwood smuggler and forest brigand others who believed in or were influenced by hinduis |
m ralph waldo emerson author american transcendentalist amos bronson alcott author american transcendentalist edwin arnold british poet journalist david bohm american quantum physicist niels bohr danish physicist nobel prize winner joseph campbell american professor writer orator fritjof capra austrian born american physicist author tao of physics victor cousin french philosopher alain danielou french writer paul deussen german orientalist and sanskrit scholar influenced by schopenhauer friend of nietzsche and vivekananda will durant american philosopher and writer t s eliot anglo american author nobel prize winner rene guenon french philosopher johann gottfried herder german poet critic theologian philosopher and romanticist herman hesse german author nobel prize winner wilhelm von humboldt german linguist government functionary foreign diplomat philosopher founder of humboldt universit t william jones philologist british philologist discoverer of the indo european languages family carl jung swiss psychiatri |
st and founder of analytical psychology herman melville american author poet jules michelet french historian yehudi menuhin violinist exposed many westerners to yoga max muller german orientalist created the discipline of comparative religion friedrich nietzsche german philosopher philologist atheist and psychologist pythagoras ionian mathematician and philosopher formulated the pythagorean theorem robert oppenheimer american physicist father of the atomic bomb romain rolland french writer nobel prize winner george william russell irish nationalist critic and poet carl sagan american astronomer science popularizer promoted seti carlos santana musician arthur schopenhauer german philosopher erwin schr dinger austrian physicist nobel prize winner albert schweitzer german theologian philosopher physician nobel prize winner george bernard shaw irish playwright satirist vegetarian nobel prize winner huston smith preeminent american religious studies scholars wrote the religions of man isaac tigrett entrepreneur fo |
under of hard rock cafe leo tolstoy russian novelist reformer pacifist moral thinker vegetarian arnold joseph toynbee british historian mark twain american humorist writer and lecturer ludwig van beethoven german composer of classical music henry david thoreau author american transcendentalist paul verlaine french poet hg wells british science fiction writer vegetarian john archibald wheeler american theoretical physicist alfred north whitehead british american philosopher physicist and mathematician walt whitman american poet and humanist william butler yeats irish poet dramatist mystic public figure nobel prize winner houman younessi iranian born australian american scientist activist see also list of people by belief hinduism lists of people by belief hinduism related lists leviticus is the third book of the hebrew bible also the third book in the torah five books of moses christians refer to the hebrew bible as the old testament the english name is derived from the latin liber leviticus which is from the |
greek i e in jewish writings it is customary to cite the book by its first word vayikra and he called vayikra is also the name of the first weekly torah reading or parshah in the book the main points of the book are concerned with legal rules and priestly ritual despite the english title of the work it is important to note that the book makes a very strong distinction between the priesthood who are identified as being descended from aaron and mere levites summary the book is generally considered to consist of two large sections both of which contain several mitzvot and thus the work constitutes a major source of jewish law the first part leviticus one one six and leviticus two seven constitutes the main portion of the priestly code which describes the details of rituals and of worship as well as details of ritual cleanliness and uncleanliness within this section are laws regarding the regulations for different types of sacrifice leviticus one seven burnt offerings meat offerings and thank offerings leviticus |
one three sin offerings and trespass offerings leviticus four five priestly duties and rights concerning the offering of sacrifices leviticus six seven the practical application of the sacrificial laws within a narrative of the consecration of aaron and his sons leviticus eight one zero aaron s first offering for himself and the people leviticus eight the case law lesson of strange fire being offered by nadab and abihu and their subsequent execution by yahweh for doing so leviticus nine one zero laws concerning purity and impurity leviticus one one one six laws about clean and unclean animals leviticus one one laws concerning ritual cleanliness after childbirth leviticus one two laws concerning tzaraath of people and of clothes and houses often translated as leprosy and mildew respectively leviticus one three one four laws concerning bodily discharges such as blood pus etc and purification leviticus one five laws regarding a day of national atonement yom kippur leviticus one six laws concerning the commutatio |
n of vows leviticus two seven the second part leviticus one seven two six is known as the holiness code and places particular and noticeable emphasis on holiness and the holy it is notably more of a miscellany of laws within this section are laws concerning idolatry the slaughter of animals dead animals and the consumption of blood leviticus one seven laws concerning sexual conduct including some that are often interpreted as referring to male homosexuality sorcery and moloch leviticus one eight and also leviticus two zero in which penalties are given laws concerning molten gods peace offerings scraps of the harvest fraud the deaf blind elderly and poor poisoning the well hate sex with slaves self harm shaving prostitution sabbaths sorcery familiars strangers and just weights and measure leviticus one nine laws concerning priestly conduct and prohibitions against the disabled ill and superfluously blemished from becoming priests or becoming sacrifices for descendants of aaron and animals respectively leviticu |
s two one two two laws concerning the observation of the annual feasts and the sabbath leviticus two three laws concerning the altar of incense leviticus two four one nine the case law lesson of a blasphemer being stoned to death and other applications of the death penalty leviticus two four one zero two three laws concerning the sabbath and jubilee years leviticus two five a hortatory conclusion to the section giving promises regarding obedience to these commandments and warnings and threats for those that might disobey them these ordinances in the book are said to have been delivered in the space of a month specifically the first month of the second year after the exodus a major chiastic structure runs through practically all of this book for more detailed information see the article on chiastic structure religious interpretation jewish views orthodox jews believe that this entire book is the word of god dictated by god to moses on mount sinai in talmudic literature there is evidence that this is the first |
book of the tanakh which was taught in the rabbinic system of education in talmudic times a possible reason may be that of all the books of the torah leviticus is the closest to being purely devoted to mitzvot and its study is thus able to go hand in hand with their performance there are two main midrashim on leviticus the halakhic one sifra and a more aggadic one vayikra rabbah christian views after the christian era began parts of leviticus began to be interpreted by christians as prophecy of the coming of their messiah jesus to many christian readers leviticus is not literally about law or regulations for worship but instead a prophecy prefiguring jesus regarding in particular his crucifixion as a sin offering this interpretation is scripturally referred to within the epistle to the hebrews and leviticus is said to contain in its law a gospel of the grace of god christians state that no one before the time of jesus was able to fully understand this academic context most modern scholars of biblical criticis |
m support the documentary hypothesis in this almost the entirity of leviticus is identified as being from a single earlier document the priestly source while this source is said to originate amongst the aaronid priesthood leviticus is nethertheless said to consist of several layers of accretion from earlier collections of laws the base of this accretion is identified in the hypothesis as the holiness code regarded as an early independent document having a faint relationship with the covenant code presented earlier in the bible the priestly source is envisioned as a later rival version of the stories contained within je and the holiness code thus being the law code that the priestly source presented as being dictated to moses at sinai in the place of the covenant code on top of this over time different writers of varying levels of narrative competence ranging from repetetive tedium to case law inserted laws some from earlier independent collections these additional laws in critical scholarship are those which |
subsequently formed the priestly code and thus the other portion of leviticus see also torah the bible and homosexuality external links online translations of leviticus original text vayikra leviticus hebrew english at mechon mamre org jewish translations leviticus at mechon mamre jewish publication society translation leviticus the living torah rabbi aryeh kaplan s translation and commentary at ort org vayikra leviticus judaica press translation with rashi s commentary at chabad org christian translations leviticus at the great books new revised standard version translations identifying sources according to the documentary hypothesis leviticus with sources highlighted at wikisource the law code of leviticus isolated at wikisource the description of priestly ritual in isolation at wikisource related article book of leviticus article jewish encyclopedia torah tabernacle and jerusalem temples old testament books lyman frank baum may one five one eight five six may six one nine one nine was an american author ph |
ilatelist and the creator along with illustrator w w denslow of one of the most popular books ever written in american children s literature the wonderful wizard of oz l frank baum baum s childhood and early life frank was born in chittenango new york into a protestant family of german origin the seventh of nine children born to cynthia stanton and benjamin ward baum only five of whom survived into adulthood he was named lyman after his father s brother but always disliked this name and preferred to go by frank his mother cynthia stanton was a direct descendant of thomas stanton one of the four founders of what is now stonington connecticut benjamin baum was a wealthy businessman who had made his fortune in the oil fields of pennsylvania frank grew up on his parents expansive estate rose lawn which he always remembered fondly as a sort of paradise as a young child frank was tutored at home with his siblings but at the age of one two he was sent to study at peekskill military academy frank was a sickly child g |
iven to daydreaming and his parents may have thought he needed toughening up but after two utterly miserable years at the military academy following an incident described as a heart attack he was allowed to return home frank started writing at an early age perhaps due to an early fascination with printing his father bought him a cheap printing press and frank used it to produce the rose lawn home journal with the help of his younger brother harry clay baum with whom he had always been close the brothers published several issues of the journal and were even able to sell ads by the time he was one seven baum had established a second amateur journal the stamp collector printed an one one page pamphlet called baum s complete stamp dealers directory and started a stamp dealership with his friends at about the same time frank embarked upon his lifetime infatuation with theater and the performing arts a devotion which would repeatedly lead him to failure and near bankruptcy his first such failure occurred at age one |
eight when a local theatrical company duped him into replenishing their stock of costumes with the promise of leading roles that never came his way disillusioned baum left the theatre temporarily and went to work as a clerk in his brother in law s dry goods company in syracuse at the age of two zero baum took on a new vocation the breeding of fancy poultry which was a national craze at the time he specialized in raising a particular breed of fowl the hamburg chicken in one eight eight zero he established a monthly trade journal the poultry record and in one eight eight six when baum was three zero years old his first book was published the book of the hamburgs a brief treatise upon the mating rearing and management of the different varieties of hamburgs yet baum could never stay away from the stage long he continued to take roles in plays performing under the stage names of louis f baum and george brooks in one eight eight zero his father made him manager of a string of theaters that he owned and baum set ab |
out writing plays and gathering a company to act in them the maid of arran a melodrama based on william blacks novel a princess of thule proved a great success baum not only wrote the play but composed songs for it and acted in the leading role on november nine one eight eight two baum married maud gage a daughter of matilda joslyn gage a then famous women s suffrage activist the south dakota years in july one eight eight eight baum and his wife moved to aberdeen south dakota where he opened a store baum s bazaar his habit of giving out wares on credit led to the eventual bankrupting of the store so baum turned to editing a local newspaper the aberdeen saturday pioneer where he wrote a famous column our landlady baum s description of kansas in the wonderful wizard of oz is based on his experiences in drought ridden south dakota baum becomes an author promotional poster for baum s popular books for children one nine zero one after baum s newspaper failed in one eight nine one he and his family moved to chicago |
illinois where baum took a job reporting for the evening post for several years he edited a magazine for advertising agencies focused on window displays in stores the major department stores created elaborate christmas time fantasies using clockwork mechanism that made it seem that people were moving children thought it was magic and adults wondered if there was not a man behind the curtain pulling the levers in one eight nine seven he wrote and published mother goose in prose a collection of mother goose rhymes written as prose stories and illustrated by maxfield parrish mother goose was a moderate success and allowed baum to quit his door to door job in one eight nine nine baum partnered with illustrator w w denslow to publish father goose his book a collection of nonsense poetry the book was a success becoming the best selling children s book of the year the baum denslow mother goose book used as free premium for breakfast cereal the wonderful wizard of oz baum and denslow were deeply involved in both the |
politics of the one eight nine zero s and the images that were used drawing on this experience they constructed a modern fairy tale in one nine zero zero baum and denslow with whom he shared the copyright published the wonderful wizard of oz to much critical and financial acclaim the book was the bestselling children s book for two years after its initial publication baum went on to write thirteen other novels based on the places and people of the land of oz the book was heavily influenced by landmarks in holland michigan where he would stay with his great grandfather in fact the yellow brick road was named after winding cobblestone roads in that town two years after wizard s publication baum and denslow teamed up with composer paul tietjens and director julian mitchell to produce a musical stage version of the book it ran on broadway two nine three stage nights from one nine zero two to one nine one one and also successfully toured the united states the stage version starred dave montgomery and fred stone a |
s the tin woodman and scarecrow respectively which shot the pair to instant fame at the time the stage version differed quite a bit from the book and was aimed primarily at adults toto was replaced with imogene the cow and tryxie tryfle a waitress and pastoria a streetcar operator were added as fellow cyclone victims baum had the actors make explicit reference to president theodore roosevelt senator mark hanna and oil magnate john d rockefeller later life and work with the success of wizard baum and denslow hoped lightning would strike a third time and in one nine zero one published dot and tot of merryland the book was one of baum s weakest and its failure further strained his faltering relationship with denslow it would be their last collaboration several times during the development of the oz series baum declared that he had written his last oz book and devoted himself to other works of fantasy fiction based in other magical lands including the life and adventures of santa claus and queen zixi of ix howeve |
r persuaded by popular demand letters from children and the failure of his new books he returned to the series each time all of his novels have fallen into public domain in most jurisdictions and many are available through project gutenberg later in life baum was plagued with debt and illness because of his lifelong love of theatre he often financed elaborate musicals often to his financial detriment one of baum s worst financial endeavors was his fairylogues and radio plays one nine zero eight which combined a slideshow film and live actors with a lecture by baum as if he were giving a travelogue to oz however baum ran into trouble and could not pay his debts to the company who produced the films and did not get back to a stable financial situation until almost a decade later after he sold the royalty rights to many of his earlier works including the wonderful wizard of oz his final book glinda of oz was published a year after his death in one nine two zero but the oz series was continued long after his deat |
h by other authors notably ruth plumly thompson who wrote an additional nineteen oz books baum made use of several pseudonyms for some of his other non oz books they include edith van dyne the aunt jane s nieces series laura bancroft twinkle and chubbins policeman bluejay floyd akers the sam steele series suzanne metcalf annabel schuyler staunton daughters of destiny john estes cooke capt hugh fitzgerald baum also anonymously wrote the last egyptian a romance of the nile baum died on may six one nine one nine aged six three and was buried in the forest lawn memorial park cemetery in glendale california baum s beliefs politics during the events leading up to the wounded knee massacre baum wrote a racist editorial for the saturday pioneer stating that the native americans whom he described as whining curs in sharp contrast to the opening lines of the same editorial in which he speaks respectfully of sitting bull and expressed contempt for the behavior of white men toward him should be completely annihilated aft |
er the massacre he wrote a second editorial repeating his earlier opinion and criticizing the government for not taking even harsher measures wipe these untamable creatures from the face of the earth it should be noted that these editorials are the only known occasion on which baum expressed such views and that he wrote them when his own fortunes were declining some of baum s work as a children s author including two of his oz books have been criticized for perpetuating racist stereotypes about african americans a contradictory opinion points out that his overall writing is remarkably inclusive and his characters diverse though vocabulary was racist by today s standards he did at least acknowledge americans of non european ancestry and much of his writing such as the short story the enchanted buffalo which purports to be a native american fable speaks with utmost respect for tribal peoples it is unfortunate that these two short editorials written when he was ill and the community was living in terror continue |
to haunt his legacy sitting bull was an indian with a white man s spirit of hatred and revenge for those who had wronged him and his in his day he saw his son and his tribe gradually driven from their possessions forced to give up their old hunting grounds and espouse the hard working and uncongenial avocations of the whites and these his conquerors were marked in their dealings with his people by selfishness falsehood and treachery what wonder that his wild nature untamed by years of subjection should still revolt what wonder that a fiery rage still burned within his breast and that he should seek every opportunity of obtaining vengeance upon his natural enemies the proud spirit of the original owners of these vast prairies inherited through centuries of fierce and bloody wars for their possession lingered last in the bosom of sitting bull with his fall the nobility of the redskin is extinguished was the wizard of oz a political allegory in one nine six four a high school history teacher named henry littlef |
ield published an article in the journal american quarterly analyzing characters and elements in the wonderful wizard of oz as metaphors for political figures and events of the one eight nine zero s in particular the populist movement and debates over the gold standard many scholars economists and historians have expanded on littlefield s interpretation ever since pointing to multiple similarities between the characters especially as depicted in denslow s illustrations and stock figures from editorial cartoons of the period baum had been a political editor in the one eight nine zero s and denslow was an editorial cartoonist as well as an illustrator of children s books baum inserted a series of political references into the one nine zero two stage version such as references by name to the president and a powerful senator and to john d rockefeller for providing the oil needed by the tin woodman scholars have found few political references in baum s oz books after one nine zero two when baum himself was asked w |
hether his stories had hidden meanings he always replied that they were written to please children and generate an income for his family as a staunch republican and avid supporter of women s suffrage baum personally did not support the political ideals of either the populist movement of one eight nine zero nine two or the bryanite silver movement of one eight nine six one nine zero zero he published a poem in support of william mckinley whether this invalidates the political interpretation or not depends in part on the reader s attitude towards authorial intent and what literary critics have termed the intentional fallacy most fans of the oz books reject any political interpretation since lovers of baum s fantasy and students of america in the one eight nine zero s approach the text with different intentions it is perhaps not surprising that they come to different interpretations religion originally a methodist baum joined the episcopal church in aberdeen in order to participate in community theatricals later |
he and his wife became theosophists in one eight nine seven baum s beliefs are often reflected in his writing the only mention of a church in the oz books is the porcelain one which dorothy knocks over in the china country in the wizard of oz the baums also sent their older sons to ethical culture sunday school in chicago which taught morality but not religion miscellaneous anecdotes when the wardrobe department of mgm began to buy costumes for the one nine three nine movie version of the wizard of oz they purchased second hand clothes from rummage sales around hollywood actor frank morgan who played the wizard was given one such second hand overcoat to wear and he happened to notice that the lining of the coat had a label saying property of l frank baum in early publicity for the movie mgm emphasized that this was a true story soon after the movie was released the coat was taken to baum s wife who confirmed that it had been his see a very popular myth about the origin of the name oz is that it was inspired |
by the labels on the author s filing cabinet a n o z less popular is the myth that it stood for the abbreviation for ounce however according to the international wizard of oz club l frank baum s widow maud once wrote to writer jack snow on this subject and stated that it was just a name that frank had created out of his own mind john ritter portrayed baum in a one nine nine zero made for tv movie the dreamer of oz the l frank baum story the film was largely fiction but retain some of the basic details of baum s life such as his the many failures of his adult life before oz and a few of the elements that inspired the books bibliography for oz books please see list of oz books princess truella a character from the magical monarch of mo non oz works the maid of arran play one eight eight two the book of hamburgs poultry guide one eight nine six by the candelabra s glare poetry one eight nine seven mother goose in prose prose retellings of mother goose rhymes one eight nine seven father goose his book nonsense po |
etry one eight nine nine the army alphabet one nine zero zero the navy alphabet one nine zero zero songs of father goose father goose set to music one nine zero zero the art of decorating dry goods windows and interiors trade publication one nine zero zero dot and tot of merryland fantasy one nine zero one american fairy tales fantasy one nine zero one the master key an electric fairy tale fantasy one nine zero one the life and adventures of santa claus one nine zero two the magical monarch of mo fantasy one nine zero three originally published in one nine zero zero as a new wonderland the enchanted island of yew fantasy one nine zero three a kidnapped santa claus one nine zero four queen zixi of ix fantasy one nine zero five john dough and the cherub fantasy one nine zero six the sea fairies fantasy one nine one one sky island fantasy one nine one two under pseudonyms as edith van dyne aunt jane s nieces one nine zero six aunt jane s nieces abroad one nine zero six aunt jane s nieces at millville one nine ze |
ro eight aunt jane s nieces at work one nine zero six aunt jane s nieces in society one nine one zero aunt jane s nieces and uncle john one nine one one the flying girl one nine one one aunt jane s nieces on vacation one nine one two the flying girl and her chum one nine one two aunt jane s nieces on the ranch one nine one three aunt jane s nieces out west one nine one four aunt jane s nieces in the red cross one nine one five republished in one nine one eight mary louise one nine one six mary louise in the country one nine one six mary louise solves a mystery one nine one six mary louise and the liberty girls one nine one eight mary louise adopts a soldier one nine one nine as laura bancroft the twinkle tales one nine zero six policeman bluejay one nine zero seven anonymous the last egyptian a romance of the nile one nine zero eight references baum frank joslyn macfall russell p one nine six one to please a child chicago reilly lee co rogers katharine m two zero zero two l frank baum creator of oz st martin |
s press isbn zero three one two three zero one seven four x riley michael o one nine nine seven oz and beyond the fantasy world of l frank baum university of kansas press isbn zero seven zero zero six zero eight three two x external links international wizard of oz club eric gjovaag s oz page lyman frank baum at classicauthors net the online books page an online library of literature more on the story about l frank baum s coat the wonderful website of oz text of baum s books and links to related sites free audiobook road to oz from librivox l frank baum discusses baum s works oz and other german fanpage free audiobook of the marvelous land of oz from librivox one eight five six births one nine one nine deaths american journalists american children s writers german americans american fantasy writers oz writers burials at forest lawn memorial park cemetery syracusians new york map of lake ladoga towpath bridge between lake ladoga and lake onega from a photograph taken ca one nine one two lake ladoga russian lad |
ozhskoye ozero finnish laatokka is the largest lake in europe located in karelia and leningrad oblast in northwestern russia near the border with finland the area of the lake is one seven seven zero zero km approximately six eight zero zero square miles it has about six six zero islands with the total area of four three five km most of the islands are situated near the northwestern coast including the famous valaam islands the lake drains into the gulf of finland of the baltic sea via river neva the area of its basin is two seven six zero zero zero km the basin of the ladoga lake includes about five zero zero zero zero lakes and three five zero zero rivers longer than one zero km about eight five of the water income is due to the three most important tributaries river svir from lake onega south east river vuoksi from lake saimaa in finland west volkhov river from lake ilmen south ladoga has its own endemic ringed seal subspecies the two zero zero three film vozvrashcheniye directed by andrei zvyagintsev was f |
ilmed on and around lake ladoga and the gulf of finland history the lake formed an important part of the trade route from the varangians to the greeks the oldest russian capital old ladoga took its name from the lake the ancient valaam monastery was founded on the island of valaam finnish valamo the largest in lake ladoga abandoned between one six one one one seven one five magnificently restored in the one eight th century and evacuated to finland during the winter war in one nine four zero in one nine eight nine the monastic activities in the valaam were resumed other historic cloisters in the vicinity are the konevets monastery which sits on another island and the alexander svirsky monastery which preserves fine samples of medieval muscovite architecture between one six one seven one seven two one the swedish russian border was drawn through lake ladoga then later one eight one two one nine four zero the border between finland and russia during the siege of leningrad one nine four one one nine four four la |
ke ladoga provided the only access to the besieged city supplies were transported into leningrad with trucks on winter roads over the ice the road of life and by boat in the summer karelia lakes of russia current distribution of human language families most languages are known to belong to language families an accurately identified family is a phylogenetic unit that is all its members derive from a common ancestor this ancestor is very seldom known to us directly since most languages have a very short recorded history however it is possible to recover many of its features by applying the comparative method a reconstructive procedure worked out by one nine th century linguist august schleicher this can demonstrate the validity of many of the proposed families listed below language families can be divided into smaller phylogenetic units conventionally referred to as branches of the family because the history of a language family is often represented as a tree diagram however the term family is not restricted to |
any one level of this tree the germanic family for example is a branch of the indo european family some taxonomists do restrict the term family to a certain level but there is little consensus in how to do this those who do affix such labels also subdivide branches into groups and groups into complexes they also aggregate families into phyla also known as stocks or superfamilies phyla are often used to aggregate american indian language families one method for doing all of this is called glottochronology the common ancestor of a family is known as its protolanguage for example the reconstructible protolanguage of the well known indo european family is called proto indo european this is not known from written records since it was spoken before the invention of writing but sometimes a protolanguage can be identified with a historically known language thus provincial dialects of latin vulgar latin gave rise to the modern romance languages so the proto romance language is more or less identical with latin if not |
exactly with the literary latin of the classical writers and dialects of old norse are the protolanguage to norwegian swedish danish faroese and icelandic languages that cannot be reliably classified into any family are known as language isolates a language isolated in its own branch within a family such as greek within indo european is often also called an isolate but such cases are usually clarified for instance greek might be referred to as an indo european isolate largest families according to the numbers in ethnologue the largest language families in terms of number of languages are niger congo one five one four languages austronesian one two six eight languages trans new guinea five six four languages validity disputed indo european four four nine languages sino tibetan four zero three languages afro asiatic three seven five languages nilo saharan two zero four languages pama nyungan one seven eight languages oto manguean one seven four languages number disputed lyle campbell includes only two seven au |
stro asiatic one six nine languages sepik ramu one zero zero languages validity disputed tai kadai seven six languages tupi seven six languages dravidian seven three languages mayan six nine languages language families spoken in the following each bulleted item is a known language family the geographic headings over them are meant solely as a tool for grouping families into collections more comprehensible than an unstructured list of the dozen or two of independent families geographic relationship is convenient for that purpose but these headings are not a suggestion of any super families phylogenetically relating the families named africa and southwest asia image african languages png afro asiatic languages formerly hamito semitic niger congo languages sometimes niger kordofanian nilo saharan languages khoisan languages or khoi san europe and north west and south asia indo european languages dravidian languages some include dravidian languages in a larger elamo dravidian language family the non genetic class |
of caucasian languages which is generally thought to include at least two at most tenuously related families north caucasian south caucasian or kartvelian altaic languages the status of the altaic languages is disputed turkic languages are clearly spoken in this region uralic languages hurro urartian languages extinct yukaghir languages some include yukaghir in the uralic family chukotko kamchatkan languages yeniseian languages andamanese languages two families east southeast asia and the pacific austroasiatic languages austronesian malayo polynesian languages hmong mien languages japonic languages or fuyu languages papuan languages multiple unrelated families sino tibetan languages tai kadai languages boka choda kobi australian aboriginal languages bunaban languages daly languages limilngan languages djeragan languages nyulnyulan languages wororan languages mindi languages arnhem land languages three families and two isolates gunwinyguan languages pama nyungan languages north america distribution of languag |
e families and isolates north of mexico at first contact see main article native american languages algic languages incl algonquian languages two nine alsean languages two caddoan languages five chimakuan languages two chinookan languages three chumashan languages six comecrudan languages three coosan languages two eskimo aleut languages seven guacurian languages a k a waikurian eight iroquoian languages one one kalapuyan languages three kiowa tanoan languages seven maiduan languages four mayan languages north america northeast mexico esselen us california haida canada british columbia us alaska karankawa us texas karok a k a karuk us california keres us new mexico kootenai canada british columbia us idaho montana natchez us mississippi louisiana sometimes linked to muskogean salinan us california siuslaw us oregon takelma us oregon timucua us florida georgia tonkawa us texas tunica us mississippi louisiana arkansas washo us california nevada yana us california yuchi us georgia oklahoma zuni a k a shiwi us ne |
w mexico australia enindhilyagwa aka andilyaugwa anindilyakwa laragiya minkin extinct perhaps a member of yiwaidjan or tankic ngurmbur perhaps a member of macro pama nyungan tiwi melville and bathurst islands asia ainu language or languages russia japan like arabic or japanese the diversity within ainu is large enough that some consider it to be perhaps up to a dozen languages while others consider it a single language with high dialectal diversity burushaski pakistan india sometimes linked to yeniseian kalto or nahali india sometimes linked to munda korean north part of the poorly attested tyrrhenian family unclassified languages many languages are too poorly attested to classify many of them are extinct and never will be known well enough to classify some may have been isolates others were likely members of established families europe iberian spain extinct tartessian spain portugal extinct africa shabo meroitic extinct asia quti extinct kaskian extinct cimmerian extinct south america baenan brazil extinct c |
ulle peru extinct cunza chile bolivia argentina extinct gamela brazil maranh o extinct gorgotoqui bolivia extinct huamo brazil pernambuco extinct kukur brazil mato grosso extinct nat brazil pernambuco extinct tarairi brazil rio grande do norte tux brazil bahia pernambuco extinct xok brazil alagoas pernambuco extinct xukur brazil pernambuco para ba extinct north america adai us louisiana texas extinct alag ilac guatemala aranama tamique us texas extinct atakapa us louisiana texas extinct beothuk canada newfoundland extinct calusa us florida extinct cayuse us oregon washington extinct cotoname northeast mexico us texas extinct maratino northeastern mexico extinct naolan mexico tamaulipas extinct quinigua northeast mexico extinct solano northeast mexico us texas extinct sign languages see also list of sign languages although deaf sign languages have emerged naturally in deaf communities alongside or among spoken languages they are unrelated to spoken languages and have different grammatical structures at their c |
ore a group of sign languages known as manually coded languages are more properly understood as signed modes of spoken languages and therefore belong to the language family of the spoken language one example of such a signed language is warlpiri sign language there has been very little historical linguistic research on sign languages and few attempts to determine genetic relationships between sign languages other than simple comparison of lexical data and some discussion about whether certain sign languages are dialects of a language or languages of a family auslan nzsl and bsl are usually considered to belong to a language family known as banzsl and japanese sign language taiwanese sign language and korean sign language are thought to be members of a japanese sign language family there are a number of sign languages that emerged from old french sign language and might tentatively be considered a part of a french sign language family french sign language quebec sign language american sign language irish sign |
language dutch sign language flemish sign language belgian french sign language mexican sign language and others bolivian sign language is sometimes considered a dialect of american sign language and thus would also belong with this group other languages such as nicaraguan sign language al sayyid bedouin sign language and providence island sign language are known to be isolates creole languages pidgins mixed languages and trade languages american indian pidgin english basque algonquian pidgin a k a micmac basque pidgin souriquois bislamic languages australian creole a k a kriol bislama pijin tok pisin torres strait creole a k a broken cape york creole lockhart creole broken oghibbeway a k a broken ojibwa broken slavey a k a slavey jargon broken slav callahuaya a k a machaj juyai kallawaya carib pidgin a k a ndjuka amerindian pidgin ndjuka trio carib pidgin arawak mixed language catalangu chabacano a spanish creole spoken in south of the philippines chinook jargon delaware jargon a k a pidgin delaware eskimo t |
rade jargon a k a herschel island eskimo pidgin ship s jargon greenlandic eskimo pidgin guajiro spanish g eg ence nicarao haida jargon haitian creole hawaiian creole english hiri motu hudson strait pidgin international sign or gestuno constructed language inuktitut english pidgin jargonized powhatan kutenai jargon labrador eskimo pidgin a k a labrador inuit pidgin lingua franca apalachee lingua franca creek lingua franca lingua geral do sul a k a lingua geral paulista tup austral loucheux jargon a k a jargon loucheux media lengua mednyj aleut a k a copper island aleut medniy aleut cia michif a k a french cree m tis metchif mitchif m tchif mobilian jargon a k a mobilian trade jargon chickasaw chocaw trade language yam montagnais pidgin basque a k a pidgin basque montagnais nheengat a k a lingua geral amaz nica lingua boa lingua bras lica lingua geral do norte norfuk nootka jargon ocaneechi pitkern pidgin massachusett portuguese based creole languages rusnorsk sango proposed language stocks see also endangered |
language extinct language constructed language external links http www ethnologue com web asp http gebaren ugent be http www elanguages info articles products isbn zero five two one two nine eight seven five x ruhlen merritt one nine eight seven a guide to the world s languages stanford stanford university press sturtevant william c ed one nine seven eight present handbook of north american indians vol one two zero washington d c smithsonian institution vols one three one six one eight two zero not yet published voegelin c f voegelin f m one nine seven seven classification and index of the world s languages new york elsevier language families lists of languages looe island also known as st george s island is a small island a mile from the mainland town of looe in cornwall until recently it was owned and inhabited by two elderly sisters babs and evelyn atkins who have made a gift of the island to the cornwall wildlife trust in perpetuity it is an island of outstanding natural beauty about two two five acres ni |
ne one zero zero zero m in area and a mile one six km in circumference the highest point is four seven m above sea level with frost and snow virtually unknown it has an exceptionally mild climate daffodils bloom at christmas and unlike most small islands it is partly wooded a natural sanctuary for sea and woodland birds and one time haunt to smugglers its history includes a benedictine chapel built in one one three nine of which only a few stones remain visible legend has it that joseph of arimathea landed here with the child christ evelyn atkins wrote two books we bought an island one nine seven six and its sequel tales from our cornish island one nine eight six about the purchase of the island and what it is like to live there she died in one nine nine seven at the age of eight seven but her sister babs continued to live on the island until her death in two zero zero four at the age of eight six leaving the island to the cornwall wildlife trust who will preserve it as a nature reserve the island is normally |
accessible only by boat but at low spring tides it is just about possible for the journey to be made by foot across the rocky sea floor the island is open to day visitors a landing fee is payable during the summer this is a non profit making venture the landing fees and other income being devoted to conserving the island s natural beauty and to providing facilities for visitors without commercialising it in any way external links website with photos smuggling history cornwall islands of england islands in english channel latex written as latex in plain text is a document preparation system for the tex typesetting program it offers programmable desktop publishing features and extensive facilities for automating most aspects of typesetting and desktop publishing including numbering and cross referencing tables and figures page layout bibliographies and much more latex was originally written in one nine eight four by leslie lamport and has become the dominant method for using tex few people write in plain tex a |
nymore the current version is latex two the latex logo typeset with latex pronunciation latex is usually pronounced or like lay tek the last character in the name comes from a capital chi as the name of tex derives from the greek skill art technique while tex s creator donald knuth promoted the pronunciation lamport has said he doesn t favor or deprecate any pronunciation for latex it is traditionally printed with the special typographical logo shown on this page in media where the logo cannot be precisely reproduced in running text the word is typically given the unique capitalization latex to avoid confusion with the word latex the typesetting system pdf document typeset using latex displayed in apple computer s preview application on mac os x v one zero four latex is based on the idea that authors should be able to concentrate on writing within the logical structure of their document rather than spending their time on the details of formatting it encourages the separation of layout from content whilst stil |
l allowing manual typesetting adjustments where needed because the author specifies the logical structure of the document and lets the latex system worry about the presentation it is often regarded as superior to word processors and most other desktop publishing systems which allow trivially easy visual layout changes but tend to intertwine content and form so tightly that consistency and automation are often difficult latex also provides great flexibility in formatting while maintaining the identity of structure which purely structural systems like sgml and xml do not directly address latex can be arbitrarily extended by using the underlying macro language for developing custom formats for example there are numerous commercial implementations of the whole tex system which includes latex and vendors may offer extra features like phone support and additional typefaces lyx is a free visual document processor that uses latex for a back end texmacs is a free wysiwyg editor with similar functionalities as latex bu |
t a different typesetting engine a number of popular commercial dtp systems use modified versions of the original tex typesetting engine the recent rise in popularity of xml systems and the demand for large scale batch production of publication quality typesetting from such sources has seen a steady increase in the use of latex the example below shows an example of a latex input left and output right title date begin maketitle latex is a document preparation system for the tex typesetting program it offers programmable desktop publishing features and extensive facilities for automating most aspects of typesetting and desktop publishing including numbering and cross referencing tables and figures page layout bibliographies and much more latex was originally written in one nine eight four by leslie lamport and has become the dominant method for using tex few people write in plain tex anymore the current version is latexe newline this is a comment it is not shown in the final output the following shows a little |
of the typesetting power of latex begin e in house typesetting styles the popularity of latex in the technical and academic communities is perhaps partly due to its early availability on unix systems and the comparative unavailability of competing word processors on those platforms until recently but from an early stage latex was available on a wider range of hardware and software than any other program and versions are now available for almost any system from pdas to desktop pcs to supercomputers latex is less popular than mainstream desktop publishing software outside the technical communities for several reasons it is regarded as hard to learn for people with no previous experience of markup languages although it is very easy to customise the appearance of articles books and reports using only a handful of instructions it remains basically a typesetter for automating document production not a manual page design program so performing complex visual layouts incorporating multiple images is difficult another |
barrier to usage for many is the asynchronous interface used in most free versions where editing is done in a different window from the typeset display inverse search can be used to bridge this problem partially several commercial implementations however use a synchronous typographic display like other dtp systems as does the non commercial and open source lyx alternatively gnu texmacs is a free wysiwyg editor which offers features similar to latex but is based on a different typesetting engine licensing issues latex is free software it is licensed under the latex project public license lppl a license that is not compatible with the gnu general public license as it requires that modified files carry a modified filename this was done to ensure that files that depend on other files will produce the expected behavior and avoids problems similar to dll hell a new version of the lppl that will be compatible with the gpl is in the works the lppl is dfsg compliant since its version one three editors and ides there a |
re a plethora of editors and ides available so many in fact that you should be able to find one that suits your document creation style regardless of what that style is auctex an extensible package for writing and formatting tex latex files in gnu emacs and xemacs homepage bakomatex commercial realtime synchronous latex editor ftp ftp dante de tex archive systems win three two bakoma index html homepage gnu texmacs a gpl wysiwyg structured editor with similar features as latex but a different typesetting engine with tex latex import export kile ide designed mainly for kde homepage led a free environment for rapid tex latex document development under ms windows homepage lyx wysiwym what you see is what you mean ide homepage texmaker free cross platform latex editor runs on windows mac os x and unix gnu linux binary is released under the gpl license homepage texniccenter ide designed for ms windows users under gpl homepage texshop a free front end for mac os x with editor and output window homepage webtex a fre |
e miktex cgi driven web front end homepage winedt shareware ide for windows nine x nt four zero two zero zero zero xp homepage winshell freeware ide for windows nine x nt four zero two zero zero zero xp homepage tools various peripheral tools to automate latex typesetting latex two rtf translator program which is intended to convert a latex document into the rtf format latex makefile a makefile that automatically processes gnuplot and xfig files etc scientific letter commerce mail software with export to tex latex homepage distributions miktex a popular and up to date tex including latex implementation for windows oztex a popular and up to date tex including latex ams tex ams latex and revtex implementation for os x and mac os add on packages latex beamer create sophisticated structured presentations and slides using latex powerdot another very good class for presentations bussproofs sty and others a package for setting natural deduction tree proofs making a resume in latex a latex template with instructions |
for making an easily maintained resume external links community resources official latex project site website for open development of latex has links to latex two e and a beta prerelease snapshot of latex three the tex users group news comp text tex comp text tex a usenet newsgroup for la tex related questions comp text tex is an invaluable resource for la tex search the archives with google groups before posting irc irc freenode net latex latex irc chat room on freenode the comprehensive tex archive network latest la tex related packages and software periodicals the practex journal online journal of the tex users group tugboat print journal of the tex users group general tutorials latex for beginners html latex tutorials a primer pdf latex primer html getting started with latex tutorials in latex html free manual distributed by the india tex users group tug getting to grips with latex html collection of latex tutorials taking you from the very basics towards more advanced topics latex resources html a collec |
tion of tutorials and other resources from the university of cambridge advanced and in depth topics the not so short introduction to latex two e or latex two e in one three three minutes two two one mib pdf file ftp ftp ams org pub tex doc amsmath short math guide pdf the ams short math guide for latex a concise summary of math formula typesetting features pdf file case specific topics latex emacs etc for your pc html a useful and step by step guide to getting miktex and emacs working together on a windows pc tex on mac os x guide to using tex and latex on a mac reference materials the la tex encyclopaedia html help with latex html a latex concept reference the uk tex faq html frequently asked questions from comp text tex on metawiki discussion of mathmatical formulas including latex markup tex directory structure used by many la tex distributions obsolete packages and commands the companion is an excellent resource for intermediate to advanced latex users for those already somewhat familiar with latex this i |
s probably the single most useful available book on the subject the book website has the complete table of contents and a sample chapter available for download sample pages out of the book sample pages out of the book searchable version with sample pages domain specific programming languages page description languages free tex software typesetting programming languages typesetting a small selection of christian saints are listed below in alphabetical order by christian name but if necessary by surname the place or attribute part of name as well wikipedia also contains a calendar of saints listed by the day of the year on which they are traditionally venerated there are more than one zero zero zero zero roman catholic saints and beatified people among the eastern orthodox and oriental orthodox communions the numbers may be even higher since there is no fixed process of canonization and each individual jurisdiction within the two orthodox communions independently maintains parallel lists of saints that have onl |
y partial overlap note that the anglican communion has only ever canonized one saint king charles i of england see society of king charles the martyr however it recognizes pre reformation saints persons who have lead lives of celebrated sanctity or missionary zeal are included in the kalendar of the prayer book without thereby enrolling or commending such persons as saints of the church the list a b c d e f g h i j k l m n o p q r s t u v w x y z notes one the saint has been removed from the roman catholic calendar of saints due to a lack of historical evidence the removal does not mean he did not exist it is sometimes wrongly believed he was de canonized or declared not to be a saint but this is not the case and he is still so recognized two st george is specifically mentioned in the english book of common prayer from one six six two and common worship of two zero zero zero however other anglican churches have since removed reference to him or never included him in the past three the anglican feast is michae |
l and all angels four common worship has commemoration five ethiopian orthodox tewahedo church only based on a local tradition of his conversion and martyrdom see also list of canonizations for a list of catholic canonizations by date calendar of saints doctor of the church list of christians patron saint martyrology external links catholic online list of saints catholic forum patron saint index on the canonizations of john paul ii church of england common worship calendar coptic saints galleries at http st takla org the prologue from ohrid a collection of brief lives of orthodox saints along with brief homilies and meditations hagiographies hymnography and icons for many orthodox saints from the website of the orthodox church in america lists of christians saints in mathematics the lebesgue measure is the standard way of assigning a length area or volume to subsets of euclidean space it is used throughout real analysis in particular to define lebesgue integration sets which can be assigned a volume are calle |
d lebesgue measurable the volume or measure of the lebesgue measurable set a is denoted by a a lebesgue measure of is possible but even so assuming the axiom of choice not all subsets of r n are lebesgue measurable the strange behavior of non measurable sets gives rise to such statements as the banach tarski paradox a consequence of the axiom of choice examples if a is an interval a b then its lebesgue measure is the length b a the open interval a b has the same measure since the difference between the two sets has measure zero if a is the cartesian product of intervals a b and c d then it is a rectangle and its lebesgue measure is the area b a d c the cantor set is an example of an uncountable set that has the lebesgue measure of zero properties the lebesgue measure on r n has the following properties if a is a cartesian product of intervals i one i two i n then a is lebesgue measurable and lambda a i one cdot i two cdots i n here i denotes the length of the interval i if a is a disjoint union of finitely ma |
ny or countably many disjoint lebesgue measurable sets then a is itself lebesgue measurable and a is equal to the sum or infinite series of the measures of the involved measurable sets if a is lebesgue measurable then so is its complement a zero for every lebesgue measurable set a if a and b are lebesgue measurable and a is a subset of b then a b a consequence of two three and four countable unions and intersections of lebesgue measurable sets are lebesgue measurable a consequence of two and three if a is an open or closed subset of r n see metric space then a is lebesgue measurable if a is a lebesgue measurable set with a zero a null set then every subset of a is also a null set if a is lebesgue measurable and x is an element of r n then the translation of a by x defined by a x is also lebesgue measurable and has the same measure as a all the above may be succinctly summarized as follows the lebesgue measurable sets form a algebra containing all products of intervals and is the unique complete translation in |
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