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

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. E. K. Narayanan

NPTEL Co-ordinating Institute : IISc Bangalore

NPTEL Lecture Count : 62

NPTEL Course Size : 12 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

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