Title: Measure Theory and Integration By and For the Learner,
Abstract: Measure Theory and Integration is exposed with the clear aim to help
beginning learners to perfectly master its essence. In opposition of a delivery
of the contents in an academic and vertical course, the knowledge is broken
into exercises which are left to the learners for solutions. Hints are present
at any corner to help readers to achieve the solutions. In that way, the
knowledge is constructed by the readers by summarizing the results of one or a
group of exercises.
Each chapter is organized into Summary documents which contain the knowledge,
Discovery documents which give the learner the opportunity to extract the
knowledge himself through exercises and into Solution Documents which offer
detailed answers for the exercises. Exceptionally, a few number of results (A
key lemma related the justification of definition of the integral of a
non-negative function, the Caratheodory's theorem and the Lebesgue-Stieljes
measure on $\mathbb{R}^d$) are presented in appendix documents and given for
reading in small groups.
The full theory is presented in the described way. We highly expect that any
student who goes through the materials, alone or in a small group or under the
supervision of an assistant will gain a very solid knowledge in the subject and
by the way ensure a sound foundation for studying disciplines such as
Probability Theory, Statistics, Functional Analysis, etc.
The materials have been successfully used as such in normal real analysis
classes several times.