Measure theory/
Landim, Claudio 1965-
Measure theory/ Programa de Mestrado: Measure Theory Introduction: a non-measurable set Classes of subsets (semi-algebras, algebras and sigma-algebras), and set functions Set functions Caratheodory theorem Monotone classes The Lebesgue measure I & II Complete measures Approximation theorems Integration: measurable and simple functions Measurable functions Definition of the integral Integral of simple functions Properties of the integral I & II Theorems on the convergence of integrals Product measures Measure on a countable product of spaces Fubini's Theorem Hahn-Jordan Theorem Radon-Nikodym Theorem Almost sure and almost uniform Convergence in Measure Hölder and Minkowski inequalities L_p spaces From convergence in measure to convergence in L_p Bounded linear operators in L_p Vitali's covering lemma Differentiability of functions of bounded variations Absolutely continuous functions Decomposition of distribution Cantor ternary set and function Claudio Landim. - Rio de Janeiro: IMPA, 2018. - video online
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 .
Matematica.
cs
Measure theory/ Programa de Mestrado: Measure Theory Introduction: a non-measurable set Classes of subsets (semi-algebras, algebras and sigma-algebras), and set functions Set functions Caratheodory theorem Monotone classes The Lebesgue measure I & II Complete measures Approximation theorems Integration: measurable and simple functions Measurable functions Definition of the integral Integral of simple functions Properties of the integral I & II Theorems on the convergence of integrals Product measures Measure on a countable product of spaces Fubini's Theorem Hahn-Jordan Theorem Radon-Nikodym Theorem Almost sure and almost uniform Convergence in Measure Hölder and Minkowski inequalities L_p spaces From convergence in measure to convergence in L_p Bounded linear operators in L_p Vitali's covering lemma Differentiability of functions of bounded variations Absolutely continuous functions Decomposition of distribution Cantor ternary set and function Claudio Landim. - Rio de Janeiro: IMPA, 2018. - video online
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 .
Matematica.
cs