Could you please recommend some open courses on Real Analysis, mainly about Lebesgue measure and Lebesgue Integral? I am a Chinese student and will be enrolled in the course about Lebesgue integral. I want some open courses to help preview the course. A little bit content about functional analysis is okay.
Thank you!
 A: You may find this useful for real analysis, and this for functional analysis.
Moreover, you can find more video courses here about some other topics in mathematics.
If Chinese is OK to you, this course from Shanghai Jiao Tong University is acessible.
A: This course, available on Youtube, was given at IMPA.

Content:
Lecture 01: Introduction: a non-measurable set
Lecture 02: Classes of subsets (semi-algebras, algebras and sigma-algebras), and set functions
Lecture 03: Set functions
Lecture 04: Caratheodory theorem
Lecture 05: Monotone classes
Lecture 06: The Lebesgue measure
Lecture 07: The Lebesgue measure, II
Lecture 08: Complete measures
Lecture 09: Approximation theorems
Lecture 10: Integration: measurable and simple functions
Lecture 11: Measurable functions
Lecture 12: Definition of the integral
Lecture 13: Integral of simple functions
Lecture 14: Properties of the integral, 01
Lecture 15: Properties of the integral, 02
Lecture 16: Theorems on the convergence of integrals.
Lecture 17: Product measures.
Lecture 18: Measure on a countable product of spaces
Lecture 19: Fubini's Theorem
Lecture 20: Hahn-Jordan Theorem
Lecture 21: Radon-Nikodym Theorem
Lecture 22: Almost sure and almost uniform
Lecture 23: Convergence in Measure
Lecture 24: Hölder and Minkowski inequalities
Lecture 25: L_p spaces
Lecture 26: From convergence in measure to convergence in L_p
Lecture 27: Bounded linear operators in L_p
Lecture 28: Vitali's covering lemma
Lecture 29: Differentiability of functions of bounded variations
Lecture 30: Absolutely continuous functions
Lecture 31: Decomposition of distribution
Lecture 32: Cantor ternary set and function

