Learn · NPTEL

Course11110100540 lectures

Measure and Integration

Prof. Inder K Rana · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

Introduction and classes of sets

  1. L1- Introduction ,Extended Real numbers Video
  2. L2-Algebra and Sigma Algebra of a subset of a set Video
  3. L3-Sigma Algebra generated by a class Video
  4. L4-Monotone Class Video

Measure

  1. L5-Set function Video
  2. L6-The Length function and its properties Video
  3. L7-Countably additive set functions on intervals Video
  4. L8-Uniqueness Problem for Measure Video

Extension of measures

  1. L9-Extension of measure Video
  2. L10-Outer measure and its properties Video
  3. L11-Measurable sets Video

The Lebesgue measure and its properties

  1. L12-Lebesgue measure and its properties Video
  2. L13-Characterization of Lebesque measurable sets Video

Measurable functions

  1. L14-Measurable functions Video
  2. L15-Properties of measurable functions Video
  3. L16-Measurable functions on measure spaces Video

Integrations

  1. L17-Integral of non negative simple measurable functions Video
  2. L18-Properties of non negative simple measurable functions Video
  3. L19-Monotone convergence theorem & Fatou's Lemma Video
  4. L20-Properties of Integral functions & Dominated Convergence Theorem Video
  5. L21-Dominated Convergence Theorem and applications Video
  6. L22-Lebesgue Integral and its properties Video
  7. L23-Denseness of continuous function Video

Measure and integration on product spaces

  1. L24-Product measures, an Introduction Video
  2. L25-Construction of Product Measure Video
  3. L26-Computation of Product Measure-I Video
  4. L27-Computation of Product Measure-II Video
  5. L28-Integration on Product spaces Video
  6. L29-Fubini's Theorems Video

Lebesgue measure on Rn

  1. L30-Lebesgue Measure and integral on R2 Video
  2. L31-Properties of Lebesgue Measure and integral on Rn Video
  3. L32-Lebesgue integral on R2 Video

Lp-spaces

  1. L33-Integrating complex-valued functions Video
  2. L34-Lp - spaces Video
  3. L35-L2(X,S,mue) Video

Special topics

  1. L36-Fundamental Theorem of calculas for Lebesgue Integral-I Video
  2. L37-Fundamental Theorem of calculus for Lebesgue Integral-II Video
  3. L38-Absolutely continuous measures Video
  4. L39-Modes of convergence Video
  5. L40-Convergence in Measure Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Mathematics
Teacher
Prof. Inder K Rana
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
Who can watch
NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed