NOC:Measure Theory (Prof. E. K. Narayanan)


Lecture 1 - Review of Riemann integration and introduction to sigma algebras


Lecture 2 - Sigma algebras and measurability


Lecture 3 - Measurable functions and approximation by simple functions


Lecture 4 - Properties of countably additive measures


Lecture 5 - Integration of positive measurable functions


Lecture 6 - Some properties of integrals of positive simple functions


Lecture 7 - Monotone convergence theorem and Fatou's lemma


Lecture 8 - Integration of complex valued measurable functions


Lecture 9 - Dominated convergence theorem


Lecture 10 - Sets of measure zero and completion


Lecture 11 - Consequences of MCT, Fatou's lemma and DCT


Lecture 12 - Rectangles in R^n and some properties


Lecture 13 - Outer measure on R^n


Lecture 14 - Properties of outer measure on R^n


Lecture 15 - Lebesgue measurable sets and Lebesgue measure on R^n


Lecture 16 - Lebesgue sigma algebra


Lecture 17 - Lebesgue measure


Lecture 18 - Fine properties of measurable sets


Lecture 19 - Invariance properties of Lebesgue measure


Lecture 20 - Non measurable set


Lecture 21 - Measurable functions


Lecture 22 - Riemann and Lebesgue integrals


Lecture 23 - Locally compact Hausdorff spaces


Lecture 24 - Riesz representation theorem


Lecture 25 - Positive Borel measures


Lecture 26 - Lebesgue measure via Riesz representation theorem


Lecture 27 - Construction of Lebesgue measure


Lecture 28 - Invariance properties of Lebesgue measure


Lecture 29 - Linear transformations and Lebesgue measure


Lecture 30 - Cantor set


Lecture 31 - Cantor function


Lecture 32 - Lebesgue set which is not Borel


Lecture 33 - L^p spaces


Lecture 34 - L^p norm


Lecture 35 - Completeness of L^p


Lecture 36 - Properties of L^p spaces


Lecture 37 - Examples of L^p spaces


Lecture 38 - Product sigma algebra


Lecture 39 - Product measures - I


Lecture 40 - Product measures - II


Lecture 41 - Fubini's theorem - I


Lecture 42 - Fubini's theorem - II


Lecture 43 - Completeness of product measures


Lecture 44 - Polar coordinates


Lecture 45 - Applications of Fubini's theorem


Lecture 46 - Complex measures - I


Lecture 47 - Complex measures - II


Lecture 48 - Absolutely continuous measures


Lecture 49 - L^2 space


Lecture 50 - Continuous linear functionals


Lecture 51 - Radon-Nikodym theorem - I


Lecture 52 - Radon Nikodym theorem - II


Lecture 53 - Consequences of Radon-Nikodym theorem - I


Lecture 54 - Consequences of Radon-Nikodym theorem - II


Lecture 55 - Continuous linear functionals on L^p spaces - I


Lecture 56 - Continuous linear functionals on L^p spaces - II


Lecture 57 - Riesz representation theorem - I


Lecture 58 - Riesz representation theorem - II


Lecture 59 - Hardy-Littlewood maximal function


Lecture 60 - Lebesgue differentiation theorem


Lecture 61 - Absolutely continuous functions - I


Lecture 62 - Absolutely continuous functions - II