Measure theory XR5T6MNEBT

URI	`m2://res/XR5T6MNEBT`
Kind	course
Creators	Inder Kumar Rana (instructor)
Date	2017-06-16
Scope	in
Ids	course 02qyf5152:111101100

Expressions

e1: edition

Language	en
Date	2017-06-16

m1: page, IIT Bombay (record). nptel 111101100
m2: page, 2017-06-16 (record). nptel 111101100

Contents

part 1: Week 1
session 1: Lecture 1A: Introduction, Extended Real Numbers
session 2: Lecture 1B: Introduction, Extended Real Numbers
session 3: Lecture 2A: Algebra and Sigma Algebra of Subsets of a Set
session 4: Lecture 2B: Algebra and Sigma Algebra of Subsets of a Set
session 5: Lecture 3A: Sigma Algebra generated by a Class
session 6: Lecture 3B: Sigma Algebra generated by a Class
part 2: Week 2
session 7: Lecture 4A: Monotone Class
session 8: Lecture 4B: Monotone Class
session 9: Lecture 5A: Set Functions
session 10: Lecture 5B: Set Functions
session 11: Lecture 6A: The Length Function and its Properties
session 12: Lecture 6B: The Length Function and its Properties
part 3: Week 3
session 13: Lecture 7A: Countably Additive Set Functions on Intervals
session 14: Lecture 7B: Countably Additive Set Functions on Intervals
session 15: Lecture 8A: Uniqueness Problem for Measure
session 16: Lecture 8B: Uniqueness Problem for Measure
part 4: Week 4
session 17: Lecture 9A: Extension of Measure
session 18: Lecture 9B: Extension of Measure
session 19: Lecture 10A: Outer Measure and its Properties
session 20: Lecture 10B: Outer Measure and its Properties
session 21: Lecture 11A: Measurable Sets
session 22: Lecture 11B: Measurable Sets
part 5: Week 5
session 23: Lecture 12A: Lebesgue Measure and its Properties
session 24: Lecture 12B: Lebesgue Measure and its Properties
session 25: Lecture 13A: Characterization of Lebesgue Measurable Sets
session 26: Lecture 13B: Characterization of Lebesgue Measurable Sets
part 6: Week 6
session 27: Lecture 14A: Measurable Functions
session 28: Lecture 14B: Measurable Functions
session 29: Lecture 15A: Properties of Measurable Functions
session 30: Lecture 15B: Properties of Measurable Functions
session 31: Lecture 16A: Measurable Functions on Measure Spaces
session 32: Lecture 16B: Measurable Functions on Measure Spaces
part 7: Week 7
session 33: Lecture 17A: Integral of Nonnegative Simple Measurable Functions
session 34: Lecture 17B: Integral of Nonnegative Simple Measurable Functions
session 35: Lecture 18A: Properties of Nonnegative Simple Measurable Functions
session 36: Lecture 18B: Properties of Nonnegative Simple Measurable Functions
session 37: Lecture 19A: Monotone Convergence Theorem and Fatou's Lemma
session 38: Lecture 19B: Monotone Convergence Theorem and Fatou's Lemma
part 8: Week 8
session 39: Lecture 20A: Properties of Integrable Functions and Dominated Convergence Theorem
session 40: Lecture 20B: Properties of Integrable Functions and Dominated Convergence Theorem
session 41: Lecture 21A: Dominated Convergence Theorem and Applications
session 42: Lecture 21B: Dominated Convergence Theorem and Applications
part 9: Week 9
session 43: Lecture 22A: Lebesgue Integral and its Properties
session 44: Lecture 22B: Lebesgue Integral and its Properties
session 45: Lecture 23A: Product Measure, an Introduction
session 46: Lecture 23B: Product Measure, an Introduction
session 47: Lecture 24A: Construction of Product Measures
session 48: Lecture 24B: Construction of Product Measures
part 10: Week 10
session 49: Lecture 25A: Computation of Product Measure - I
session 50: Lecture 25B: Computation of Product Measure - I
session 51: Lecture 26A: Computation of Product Measure - II
session 52: Lecture 26B: Computation of Product Measure - II
part 11: Week 11
session 53: Lecture 27A: Integration on Product Spaces
session 54: Lecture 27B: Integration on Product Spaces
session 55: Lecture 28A: Fubini's Theorems
session 56: Lecture 28B: Fubini's Theorems
part 12: Week 12
session 57: Lecture 29A: Lebesgue Measure and Integral on R2
session 58: Lecture 29B: Lebesgue Measure and Integral on R2
session 59: Lecture 30A: Properties of Lebesgue Measure on R2
session 60: Lecture 30B: Properties of Lebesgue Measure on R2
session 61: Lecture 31A: Lebesgue Integral on R2
session 62: Lecture 31B: Lebesgue Integral on R2

Catalogue records

nptel: 111101100 (manifestation)
nptel_video: 111101100 (manifestation)