Math 2.0

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Measure and Integration KS4G16F7QC

URIm2://res/KS4G16F7QC
Kindcourse
CreatorsInder K Rana (instructor)
Date2015-03-05
Scopein
Idscourse 02qyf5152:111101005

Expressions

e1: edition

Languageen
Date2015-03-05
Contents
  • part 1: Introduction and classes of sets
  • session 1: L1- Introduction ,Extended Real numbers
  • session 2: L2-Algebra and Sigma Algebra of a subset of a set
  • session 3: L3-Sigma Algebra generated by a class
  • session 4: L4-Monotone Class
  • part 2: Measure
  • session 5: L5-Set function
  • session 6: L6-The Length function and its properties
  • session 7: L7-Countably additive set functions on intervals
  • session 8: L8-Uniqueness Problem for Measure
  • part 3: Extension of measures
  • session 9: L9-Extension of measure
  • session 10: L10-Outer measure and its properties
  • session 11: L11-Measurable sets
  • part 4: The Lebesgue measure and its properties
  • session 12: L12-Lebesgue measure and its properties
  • session 13: L13-Characterization of Lebesque measurable sets
  • part 5: Measurable functions
  • session 14: L14-Measurable functions
  • session 15: L15-Properties of measurable functions
  • session 16: L16-Measurable functions on measure spaces
  • part 6: Integrations
  • session 17: L17-Integral of non negative simple measurable functions
  • session 18: L18-Properties of non negative simple measurable functions
  • session 19: L19-Monotone convergence theorem & Fatou's Lemma
  • session 20: L20-Properties of Integral functions & Dominated Convergence Theorem
  • session 21: L21-Dominated Convergence Theorem and applications
  • session 22: L22-Lebesgue Integral and its properties
  • session 23: L23-Denseness of continuous function
  • part 7: Measure and integration on product spaces
  • session 24: L24-Product measures, an Introduction
  • session 25: L25-Construction of Product Measure
  • session 26: L26-Computation of Product Measure-I
  • session 27: L27-Computation of Product Measure-II
  • session 28: L28-Integration on Product spaces
  • session 29: L29-Fubini's Theorems
  • part 8: Lebesgue measure on Rn
  • session 30: L30-Lebesgue Measure and integral on R2
  • session 31: L31-Properties of Lebesgue Measure and integral on Rn
  • session 32: L32-Lebesgue integral on R2
  • part 9: Lp-spaces
  • session 33: L33-Integrating complex-valued functions
  • session 34: L34-Lp - spaces
  • session 35: L35-L2(X,S,mue)
  • part 10: Special topics
  • session 36: L36-Fundamental Theorem of calculas for Lebesgue Integral-I
  • session 37: L37-Fundamental Theorem of calculus for Lebesgue Integral-II
  • session 38: L38-Absolutely continuous measures
  • session 39: L39-Modes of convergence
  • session 40: L40-Convergence in Measure

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