Learn · Measure and Integration
Lecture 10 of 40Extension of measures
L10-Outer measure and its properties
Prof. Inder K Rana · IIT Bombay
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- Measure and Integration, IIT Bombay (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- L1- Introduction ,Extended Real numbers
- L2-Algebra and Sigma Algebra of a subset of a set
- L3-Sigma Algebra generated by a class
- L4-Monotone Class
- L5-Set function
- L6-The Length function and its properties
- L7-Countably additive set functions on intervals
- L8-Uniqueness Problem for Measure
- L9-Extension of measure
- L10-Outer measure and its properties
- L11-Measurable sets
- L12-Lebesgue measure and its properties
- L13-Characterization of Lebesque measurable sets
- L14-Measurable functions
- L15-Properties of measurable functions
- L16-Measurable functions on measure spaces
- L17-Integral of non negative simple measurable functions
- L18-Properties of non negative simple measurable functions
- L19-Monotone convergence theorem & Fatou's Lemma
- L20-Properties of Integral functions & Dominated Convergence Theorem
- L21-Dominated Convergence Theorem and applications
- L22-Lebesgue Integral and its properties
- L23-Denseness of continuous function
- L24-Product measures, an Introduction
- L25-Construction of Product Measure
- L26-Computation of Product Measure-I
- L27-Computation of Product Measure-II
- L28-Integration on Product spaces
- L29-Fubini's Theorems
- L30-Lebesgue Measure and integral on R2
- L31-Properties of Lebesgue Measure and integral on Rn
- L32-Lebesgue integral on R2
- L33-Integrating complex-valued functions
- L34-Lp - spaces
- L35-L2(X,S,mue)
- L36-Fundamental Theorem of calculas for Lebesgue Integral-I
- L37-Fundamental Theorem of calculus for Lebesgue Integral-II
- L38-Absolutely continuous measures
- L39-Modes of convergence
- L40-Convergence in Measure