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Measure and Integration

IIT Bombay, , Prof. Inder K Rana

Overview

Contents:
Need to define Lebesgue Integral,Semi-algebra, Algebra, Monotone class, Sigma-algebra, Monotone class theorem. Measure spaces.Extension of measures from algebras to the generated sigma-algebras: Measurable sets; Lebesgue Measure and its properties.

Measurable functions and their properties; Integration and Convergence theorems, Lebesgue integral, Fundamental Theorem of Calculus for Lebesgue Integrals (an outline)


Product measure spaces, Fubini's theorem
Absolute continuity of measures, Radon-Nikodym theorem Introduction
to Lp spaces, Riesz-Fischer theorem; Riesz Representation theorem for L2 spaces.

Includes

Lecture 1: Introduction ,Extended Real numbers

4.1 ( 11 )


Lecture Details

Measure and Integration by Prof. Inder K Rana ,Department of Mathematics, IIT Bombay. For more details on NPTEL visit httpnptel.iitm.ac.in

Ratings

3.4


38 Ratings
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Comments
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Sam

Excellent course helped me understand topic that i couldn't while attendinfg my college.

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Dembe

Great course. Thank you very much.

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