### Lecture 1: Introduction ,Extended Real numbers

##### Lecture Details :

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

##### Course Description :

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.

##### Other Resources

The above video lectures are presented by IITBombay, India, under the program NPTEL, there are more than 350+ NPTEL courses Online available.