Lebesgue Integration

Note: Typo at 3:56 - Infimum is greatest lower bound, not the greatest upper bound!

0:00 Introduction
0:10 Lebesgue Integral Intro
0:59 Henri Lebesgue
1:55 Background terminology
5:26 Measure theory intro
5:38 Sigma algebras
8:30 Measure
11:53 Measurable space, measure space
14:35 Properties of measure
16:12 Measure Example 1: Counting Measure
19:47 Measure Example 1 Probability Measure
22:21 Lebesgue measure
24:28 Riemann integration (review)
25:54 Problems with Riemann integration
29:27 Lebesgue integration intuition & derivation
33:20 Lebesgue integration derivation & definition cont.
36:28 Lebesgue Integral Properties
38:57 Proof of Dominated Convergence Thm
46:28 L. Int. Example 1 A Piecewise Function
50:52 L. Int. Example 2: Cantor Ternary Function
59:33 Applications

Contains: Introduction, Overview/Biography, Measure Theory Intro, Measure Examples, Problems with Riemann Integration, Derivation of Lebesgue Integration, Properties of Lebesgue Integral, Proof of Dominated Convergence Theorem, Lebesgue Integration Examples, Application & Conclusion.

Видео Lebesgue Integration канала Saraphina Forman