Measure and Integration


Lecture 1 - Introduction, Extended Real numbers


Lecture 2 - Algebra and Sigma Algebra of a subset of a set


Lecture 3 - Sigma Algebra generated by a class


Lecture 4 - Monotone Class


Lecture 5 - Set function


Lecture 6 - The Length function and its properties


Lecture 7 - Countably additive set functions on intervals


Lecture 8 - Uniqueness Problem for Measure


Lecture 9 - Extension of measure


Lecture 10 - Outer measure and its properties


Lecture 11 - Measurable sets


Lecture 12 - Lebesgue measure and its properties


Lecture 13 - Characterization of Lebesque measurable sets


Lecture 14 - Measurable functions


Lecture 15 - Properties of measurable functions


Lecture 16 - Measurable functions on measure spaces


Lecture 17 - Integral of non negative simple measurable functions


Lecture 18 - Properties of non negative simple measurable functions


Lecture 19 - Monotone convergence theorem & Fatou's Lemma


Lecture 20 - Properties of Integral functions & Dominated Convergence Theorem


Lecture 21 - Dominated Convergence Theorem and applications


Lecture 22 - Lebesgue Integral and its properties


Lecture 23 - Denseness of continuous function


Lecture 24 - Product measures, an Introduction


Lecture 25 - Construction of Product Measure


Lecture 26 - Computation of Product Measure - I


Lecture 27 - Computation of Product Measure - II


Lecture 28 - Integration on Product spaces


Lecture 29 - Fubini's Theorems


Lecture 30 - Lebesgue Measure and integral on R2


Lecture 31 - Properties of Lebesgue Measure and integral on Rn


Lecture 32 - Lebesgue integral on R2


Lecture 33 - Integrating complex-valued functions


Lecture 34 - Lp - spaces


Lecture 35 - L2(X,S,mue)


Lecture 36 - Fundamental Theorem of calculas for Lebesgue Integral - I


Lecture 37 - Fundamental Theorem of calculus for Lebesgue Integral - II


Lecture 38 - Absolutely continuous measures


Lecture 39 - Modes of convergence


Lecture 40 - Convergence in Measure