Measure theory/ Claudio Landim.
Publication details: Rio de Janeiro: IMPA, 2018.Description: video onlineOther title:- Programa de Mestrado: Measure Theory
- Introduction: a non-measurable set [Other title]
- Classes of subsets (semi-algebras, algebras and sigma-algebras), and set functions [Other title]
- Set functions [Other title]
- Caratheodory theorem [Other title]
- Monotone classes [Other title]
- The Lebesgue measure I & II [Other title]
- Complete measures [Other title]
- Approximation theorems [Other title]
- Integration: measurable and simple functions [Other title]
- Measurable functions [Other title]
- Definition of the integral [Other title]
- Integral of simple functions [Other title]
- Properties of the integral I & II [Other title]
- Theorems on the convergence of integrals [Other title]
- Product measures [Other title]
- Measure on a countable product of spaces [Other title]
- Fubini's Theorem [Other title]
- Hahn-Jordan Theorem [Other title]
- Radon-Nikodym Theorem [Other title]
- Almost sure and almost uniform [Other title]
- Convergence in Measure [Other title]
- Hölder and Minkowski inequalities [Other title]
- L_p spaces [Other title]
- From convergence in measure to convergence in L_p [Other title]
- Bounded linear operators in L_p [Other title]
- Vitali's covering lemma [Other title]
- Differentiability of functions of bounded variations [Other title]
- Absolutely continuous functions [Other title]
- Decomposition of distribution [Other title]
- Cantor ternary set and function [Other title]
- cs
Course - 32 lectures + 3 exercises solutions.
These lectures are mainly based on the books "Introduction to measure and integration" by S. J. Taylor published by Cambridge University Press There are many other very good books on the subject. Here is a partial list: M. E. Munroe Measure and Integration, second edition Addison-Wesley, 1971 Paul R. Halmos Measure Theory Graduate Text in Mathematics, volume 18 Springer, 1974 Walter Rudin Principles of Mathematical Analysis McGraw-Hill, 1987 Pedro Jesus Fernandez Medida e integração. IMPA, 2007 H. Royden, Real Analysis. New York: Collier Macmillan, 1988 .
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