# Measure and Integration

IIT Bombay, , Prof. Inder K Rana

IIT Bombay, , Prof. Inder K Rana

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.

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

Sam

Sep 12, 2018

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

Dembe

March 29, 2019

Great course. Thank you very much.