Measure and Integration (USB)

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SKU
111101005



Media Storage Type : 64 GB USB Stick

NPTEL Subject Matter Expert : Prof. Inder K Rana

NPTEL Co-ordinating Institute : IIT Bombay

NPTEL Lecture Count : 40

NPTEL Course Size : 34 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)


Lecture Titles:

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

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