Measure Theory. Instructor: Prof. Inder K. Rana, Department of Mathematics, IIT Bombay. This is a course on the concepts of Measure and Integration. The course covers lessons in Extended real numbers, Algebra and sigma algebra of a subsets of a set, Sigma algebra generated by a class, Monotone class, Set functions, Countably additive set functions on intervals, Uniqueness problem for measure, Extension of measure, Outer measure and its properties, Measurable sets, Lebesgue measure and its properties, Measurable functions, Monotone convergence theorem and Fatou's lemma, Dominated convergence theorem, Lebesgue integral and its properties, Product measure, Computation of product measure, Fubini's theorems, and Lebesgue measure and integral on R2 (from nptel.ac.in)
|Introduction, Extended Real Numbers|
Instructor: Prof. Inder K. Rana, Department of Mathematics, IIT Bombay. This is a course on the concepts of Measure and Integration.