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About this book :-
Introduction to Measure Theory and Lebesque Integration written by
Eduard Emelyanov .
Book Detail :-
Title: Introduction to Measure Theory and Lebesque Integration
Edition:
Author(s): Eduard Emelyanov
Publisher: Pragati Prakasan Meerut
Series: Integral Calculus Das Mukherjee for IIT JEE IITJEE
Year: 2019
Pages: 212
Type: PDF
Language: English
ISBN:
Country:
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Book Contents :-
Introduction to Measure Theory and Lebesque Integration written by
Eduard Emelyanov
cover the following topics.
Introduction
Measurable Functions, Signed and Complex Measures
σ-Algebras, Measurable Functions, Measures, the Egoroff Theorem, Exhaustion Argument, Vector-valued, Signed and Complex Measures, Variation of a Vector-valued, Measure Operations with Measures, the Jordan Decomposition Theorem, Banach Space of Signed Measures of Bounded Variation, Construction of the Lebesgue Integral, the Monotone Convergence Theorem, the Dominated Convergence Theorem
Lebesgue Measure on R
The Caratheodory Theorem, Lebesgue Measure on R, Lebesgue – Stieltjes Measures, the Product of Measure Spaces, the Fubini Theorem, Lebesgue Measure on Rn, Lebesgue Integral in Rn, the Lusin Theorem, Cantor Sets
Continuity of a Measure with Respect to another Measure
The Radon – Nikodym Theorem, Continuity of a Measure with Respect to another Measure, the Hahn Decomposition Theorem, H¨older’s and Minkowski’s Inequalities, Completeness, Lp-Spaces, Duals, The Liapounoff Convexity Theorem
Vector Spaces of Functions on Rn
Vector Spaces of Functions on Rn, Convolutions, Radon Measures, the Riesz Representation Theorem
Bibliography
Index
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