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 :
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.