Measure and Integration RREAZHVTQ1

URI	`m2://res/RREAZHVTQ1`
Kind	course
Creators	S. Kesavan (instructor)
Date	2022-10-10
Scope	in

Expressions

e1: edition

Language	en
Date	2022-10-10

m1: page, IMSc (record). nptel 111106161
m2: page, 2022-10-10 (record). nptel 111106161

Contents

part 1: Week 1
session 1: 1.1 - Preamble
session 2: 1.2 - Algebras of sets
session 3: 1.3 - Measures on rings
session 4: 1.4 - Outer-measure
session 5: 1.5 - Measurable sets
part 2: Week 2
session 6: 2.1 - Caratheodory's method
session 7: 2.2 - Exercises
session 8: 2.3 - Exercises
session 9: 2.4 - Lebesgue measure: the ring
session 10: 2.5 - Construction of the Lebesgue measure
session 11: 2.6 - Errata
session 12: 2.7 - The Cantor set
session 13: 2.8 - Approximation
part 3: Week 3
session 14: 3.1 - Approximation
session 15: 3.2 - Approximation
session 16: 3.3 - Translation Invariance
session 17: 3.4 - Non-measurable sets
session 18: 3.5 - Exercises
session 19: 3.6 - Measurable functions
part 4: Week 4
session 20: 4.1 - Measurable functions
session 21: 4.2 - The Cantor function
session 22: 4.3 - Exercises
session 23: 4.4 - Egorov's theorem
session 24: 4.5 - Convergence in measure
session 25: 4.6 - Convergence in measure
part 5: Week 5
session 26: 5.1 - Convergence in measure
session 27: 5.2 - Exercises
session 28: 5.3 - Integration: Simple functions
session 29: 5.4 - Non-negative functions
session 30: 5.5 - Monotone convergence theorem
session 31: 5.6 - Examples
session 32: 5.7 - Fatou's lemma
session 33: 5.8 - Integrable functions
part 6: Week 6
session 34: 6.1 - Dominated convergence theorem
session 35: 6.2 - Dominated convergence theorem: Applications
session 36: 6.3 - Absolute continuity
session 37: 6.4 - Integration on the real line
session 38: 6.5 - Examples
session 39: 6.6 - Weierstrass' theorem
session 40: 6.7 - Exercises
session 41: 6.8 - Exercises
part 7: Week 7
session 42: 7.1 - Vitali covering lemma
session 43: 7.2 - Monotonic functions
session 44: 7.3 - Functions of bounded variation
session 45: 7.4 - Functions of bounded variation
session 46: 7.5 - Functions of bounded variation
session 47: 7.6 - Differentiation of an indefinite integral
session 48: 7.7 - Absolute continuity
part 8: Week 8
session 49: 8.1 - Exercises
session 50: 8.2 - Product spaces
session 51: 8.3 - Product spaces: measurable functions
session 52: 8.4 - Product measure
session 53: 8.5 - Fubini's theorem
session 54: 8.6 - Examples
session 55: 8.7 - Examples
part 9: Week 9
session 56: 9.1 - Integration of radial functions
session 57: 9.2 - Measure of the unit ball in N dimensions
session 58: 9.3 -Exercises
session 59: 9.4 - Signed measures
session 60: 9.5 - Hahn and Jordan decompositions
session 61: 9.6 - Upper,lower and totaal variations of a signed measure; Absolute continuity
session 62: 9.7 - Absolute continuity
part 10: Week 10
session 63: 10.1 - Radon-Nikodym theorem
session 64: 10.2 - Radon-Nikodym theorem
session 65: 10.3 - Exercises
session 66: 10.4 - Lebesgue spaces
session 67: 10.5 - Examples. Inclusion questions
session 68: 10.6 - Convergence in L^p
part 11: Week 11
session 69: 11.1 - Approximation
session 70: 11.2 - Applications
session 71: 11.3 - Duality
session 72: 11.4 - Duality
session 73: 11.5 - Convolutions
session 74: 11.6 - Convolutions
part 12: Week 12
session 75: 12.1 - Convolutions
session 76: 12.2 - Exercises
session 77: 12.3 - Exercises
session 78: 12.4 - Change of variable
session 79: 12.5 - Change of variable

Catalogue records

nptel: 111106161 (manifestation)
nptel_video: 111106161 (manifestation)