
bretagnol-hubber asamaanta

soochana siddhant mein, bretagnol-hubber asamaanta dou sambhaavyata vitaran sootra _ 1 aur sootra _ 2 key beach kull bhinnata doori koo kulback-leabler vichalan sootra _ 3 key avtal aur bandhe kaary dwara seemit karati haye. seema koo prasiddh pinaskar kii asamaanta key vikalp key roop mein dekhaa jaa sakata haih jaba sootra _ 3 badaa hotaa haye (udaaharan key liye 2 seey badaa).), pinskar kii asamaanta khaali haye, jabaki bretagnol-hubber bandha huaa haye aur isaliye gair-shoonya haye. iska upayog saankhyiki aur machine learning mein soochana-saiddhaantik nichali seema koo saabit karane key liye kiya jaataa haye joe parikalpana pareekshan parr nirbhar kartaa haye.
aupchaarik bayaan.
praarambhik paribhaashaaen.
sootra _ 1 aur sootra _ 2 koo maapane yogya sthaan sootra _ 7 parr dou sambhaavyata vitaran honey dein.
yaad rakhein kii sootra _ 1 aur sootra _ 2 key beach kull bhinnata dwara paribhaashit kii gaee haye 
kulback-leabler vichalan koo nimnanusar paribhaashit kiya gayaa haih
uparokt mein, sanketan sootra _ 12 sootra _ 2 key sambandh mein sootra _ 1 kii poorna nirantarta key liye khadaa haye, aur sootra _ 15 sootra _ 2 key sambandh mein sootra _ 1 key raydon-nikodam vyutpann key liye khadaa haye.
samanya kathan.
bretagnol-hubber asamaanta kahati haih
vaikalpik sanskaran.
nimnalikhit sanskaran seedhe uparokt seema dwara nihit haye lekin kuchh lekhak ise iss tarah seey kahana pasand karate hain. 
sootra _ 19 koo koee bhee ghatana honey dein. taba
jahan sootra _ 21 sootra _ 22 kaa poorak haye.
vaastav mein, kull bhinnata kii paribhasha key anusaar, kissy bhee sootra _ 23 key liye,
punarvyavasthit karate hue, humm sootra _ 25 parr daavaa kii gaee nichali seema praapt karate hain.
pramaan.
humm tsibkov kii pustak (lemma 2.6, prishth 89) mein vichaaron key baad mukhya kathan koo saabit karate hain, joe mool pramaan seey alag haye (see dekhein.unake tark key aadhunik punah pratilekhan key liye cannon kaa nott).
pramaan dou charanon mein haih
1. kauchi-swarz kaa upayog karke saabit karein kii kull bhinnata bhattacharya gunank (asamaanta kaa dahina haath) seey sambandhit haih
2. genson kii asamaanta key chaturai seey prayog seey saabit karein kii
anuprayog key udaaharan.
pakshapaati sikke kii jatilata kaa namuna.
sawal yeh haye kii 
"ack nishpaksh sikke koo pakshapaati sikke seey alag karane key liye mujhe kitane sikke uchhaalane kii aavashyakta haye?"
maan leejiye kii aapke paas 2 sikke hain, ack uchit sikka (ausat sootra 38 key saath vitarit bernauli) aur ack sootra 39-pakshapaatpurna sikka (sootra 40). phir, cumm seey cumm sootra _ 41 (kuchh sootra _ 42 key liye) key saath sambhavana key saath pakshapaati sikke kii pehchaan karane key liye, cumm seey cumm 
iss nimn seema koo praapt karane key liye humm yeh lagu karate hain kii sootra _ 44 namoonon key dou anukramon key beach kull bhinnata doori cumm seey cumm sootra _ 45 haye. aisaa isaliye haye kyonki kull bhinnata oopari seema mein sikkon key cumm yaa adhik anuman lagaane kii sambhavana hoti haye. sootra 46 aur sootra 47 koo pratyek sikke key liye sootra 44 key sambandhit sanyukt vitaran koo darshaata haye, phir
hamaare paas haye
parinam sharton koo phir seey vyavasthit karke praapt kiya jaataa haye.
key"-sashastr daku khelon key liye soochana-saiddhaantik nimn seema.
bahu-sashastr bandit mein, kissy bhee bandit algorithm key nyuntam khed parr ack nichali seema koo bretagnol-hubber aur parikalpana pareekshan parr isake parinam kaa upayog karke saabit kiya jaa sakata haye ("bandit algorithm" kaa adhyaay 15 dekhein).
itihas.
parinam pahali baar 1979 mein jeane bretagnol aur catherine huber dwara saabit kiya gayaa thaa, aur strasberg praayiktaa seminar kii kaaryavaahi mein prakaashit kiya gayaa thaa. alekjendar saibkov kii pustak mein asamaanta key praarambhik punah prakaashan aur bretagnol aur huber key liye isake shreya koo dikhaaya gayaa haye, jise assoid key lemma key praarambhik aur cumm samanya sanskaran key roop mein prastut kiya gayaa haye (notes 2.8 dekhein). 2014 mein fanoe kii asamaanta key vistaar key parinamswarup bretagnol-huber mein nirantar sudhaar saabit huaa.