Measure Theory 7B7J82V8A2

URI	`m2://res/7B7J82V8A2`
Kind	course
Creators	E. K. Narayanan (instructor)
Date	2020-01-20
Scope	in
Ids	course 04dese585:111108135

Expressions

e1: edition

Language	en
Date	2020-01-20

m1: page, IISc Bangalore (record). nptel 111108135
m2: page, 2020-01-20 (record). nptel 111108135

Contents

part 1: Sigma algebras, Measures and Integration
session 1: Review of Riemann integration and introduction to sigma algebras
session 2: Sigma algebras and measurability
session 3: Measurable functions and approximation by simple functions
session 4: Properties of countably additive measures
session 5: Integration of positive measurable functions
part 2: Integration and convergence theorems
session 6: Some properties of integrals of positive simple functions
session 7: Monotone convergence theorem and Fatou's lemma
session 8: Integration of complex valued measurable functions
session 9: Dominated convergence theorem
session 10: Sets of measure zero and completion
part 3: Outer measure
session 11: Consequences of MCT, Fatou's lemma and DCT
session 12: Rectangles in R^n and some properties
session 13: Outer measure on R^n
session 14: Properties of outer measure on R^n
session 15: Lebesgue measurable sets and Lebesgue measure on R^n
part 4: Lebesgue measure and its properties
session 16: Lebesgue sigma algebra
session 17: Lebesgue measure.
session 18: Fine properties of measurable sets
session 19: Invariance properties of Lebesgue measure
session 20: Non measurable set
part 5: Lebesgue measure and positive Borel measures on locally compact spaces
session 21: Measurable functions.
session 22: Riemann and Lebesgue integrals
session 23: Locally compact Hausdorff spaces
session 24: Riesz representation theorem
session 25: Positive Borel measures
part 6: Lebesgue measure and invariance properties
session 26: Lebesgue measure via Riesz representation theorem
session 27: Construction of Lebesgue measure
session 28: Invariance properties of Lebesgue measure.
session 29: Linear transformations and Lebesgue measure
session 30: Cantor set
session 31: Cantor function
part 7: L^p spaces and completeness
session 32: Lebesgue set which is not Borel
session 33: L^p spaces
session 34: L^p norm
session 35: Completeness of L^p
session 36: Properties of L^p spaces
session 37: Examples of L^p spaces
part 8: Product spaces and Fubini's theorem
session 38: Product sigma algebra
session 39: Product measures I
session 40: Product measures II
session 41: Fubini's theorem I
session 42: Fubini's theorem II
part 9: Applications of Fubini's theorem and complex measures
session 43: Completeness of product measures
session 44: Polar coordinates
session 45: Applications of Fubini's theorem
session 46: Complex measures I
part 10: Complex measures and Radon-Nikodym theorem
session 47: Complex measures II
session 48: Absolutely continuous measures
session 49: L^2 space
session 50: Continuous linear functionals
session 51: Radon-Nikodym theorem I
part 11: Radon-Nikodym theorem and applications
session 52: Radon Nikodym theorem II
session 53: Consequences of Radon-Nikodym theorem I
session 54: Consequences of Radon-Nikodym theorem II
session 55: Continuous linear functionals on L^p spaces I
session 56: Continuous linear functionals on L^p spaces II
part 12: Riesz representation theorem and Lebesgue differentiation theorem
session 57: Riesz representation theorem I
session 58: Riesz representation theorem II
session 59: Hardy-Littlewood maximal function
session 60: Lebesgue differentiation theorem
session 61: Absolutely continuous functions I
session 62: Absolutely continuous functions II
part 13: Live Session
session 63: Live Session 09-03-2021
session 64: Live Session 30-03-2021

Catalogue records

nptel: 111108135 (manifestation)
nptel_video: 111108135 (manifestation)