ICTP measure theory 2018
https://www.youtube.com/watch?v=llnNaRzuvd4&list=PLo4jXE-LdDTQq8ZyA8F8reSQHej3F6RFX
视频选集
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Exercise 1- Solution of exercise 3.2.4
29:43
Exercise 2- Solution of exercise 6.4.3
05:25
Exercise 3- Solution of exercise 9.2.3
21:21
Lecture 01- Introduction- a non-measurable set
31:45
Lecture 02- Classes of subsets (semi-algebras, algebras and sigma-algebras), and
01:08:49
Lecture 03- Set functions
01:12:11
Lecture 04- Caratheodory theorem
01:45:02
Lecture 05- Monotone classes
33:17
Lecture 06- The Lebesgue measure
23:51
Lecture 07- The Lebesgue measure, II
40:37
Lecture 08- Complete measures
52:49
Lecture 09- Approximation theorems
56:24
Lecture 10- Integration- measurable and simple functions
59:58
Lecture 11- Measurable functions
47:42
Lecture 12- Definition of the integral
01:12:50
Lecture 13- Integral of simple functions
14:05
Lecture 14- Properties of the integral, 01
50:57
Lecture 15- Properties of the integral, 02
28:24
Lecture 16- Theorems on the convergence of integrals.
57:21
Lecture 17- Product measures.
58:17
Lecture 18- Measure on a countable product of spaces
01:19:50
Lecture 19- Fubini's Theorem
01:25:08
Lecture 20- Hahn-Jordan Theorem
01:20:56
Lecture 21- Radon-Nikodym Theorem
01:07:08
Lecture 22- Almost sure and almost uniform
01:36:35
Lecture 23- Convergence in Measure
47:34
Lecture 24- Hölder and Minkowski inequalities
50:17
Lecture 25- L_p spaces
44:43
Lecture 26- From convergence in measure to convergence in L_p
50:27
Lecture 27- Bounded linear operators in L_p
01:45:44
Lecture 28- Vitali`s covering lemma
01:01:02
Lecture 29- Differentiability of functions of bounded variations
01:19:10
Lecture 30- Absolutely continuous functions
01:26:07
Lecture 31- Decomposition of distribution
01:25:27
Lecture 32- Cantor ternary set and function
01:29:00
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