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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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- Abstract Algebra
- Calculus
- Differential Equations
- Engineering Mathematics
- Linear Algebra
- Math Magic
- Real Analysis