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!

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

