# Measure and Integration

- Institution: IIT Bombay
- Department: Mathematics
- Teacher: Prof. Inder K Rana
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111101005)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111101005)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [L1- Introduction ,Extended Real numbers](https://invisiblenetwork.ai/learn/nptel/111101005/2b289906226b) (Video)
2. [L2-Algebra and Sigma Algebra of a subset of a set](https://invisiblenetwork.ai/learn/nptel/111101005/5ecb6c38dcf2) (Video)
3. [L3-Sigma Algebra generated by a class](https://invisiblenetwork.ai/learn/nptel/111101005/58a94e831c55) (Video)
4. [L4-Monotone Class](https://invisiblenetwork.ai/learn/nptel/111101005/2de1172c65e0) (Video)
5. [L5-Set function](https://invisiblenetwork.ai/learn/nptel/111101005/935263217deb) (Video)
6. [L6-The Length function and its properties](https://invisiblenetwork.ai/learn/nptel/111101005/55c7911ca985) (Video)
7. [L7-Countably additive set functions on intervals](https://invisiblenetwork.ai/learn/nptel/111101005/8c1729f9138e) (Video)
8. [L8-Uniqueness Problem for Measure](https://invisiblenetwork.ai/learn/nptel/111101005/0a9b67fb6b20) (Video)
9. [L9-Extension of measure](https://invisiblenetwork.ai/learn/nptel/111101005/38d34b32159f) (Video)
10. [L10-Outer measure and its properties](https://invisiblenetwork.ai/learn/nptel/111101005/03ccdc0f6cab) (Video)
11. [L11-Measurable sets](https://invisiblenetwork.ai/learn/nptel/111101005/523d5e89aba9) (Video)
12. [L12-Lebesgue measure and its properties](https://invisiblenetwork.ai/learn/nptel/111101005/c082d5da2c66) (Video)
13. [L13-Characterization of Lebesque measurable sets](https://invisiblenetwork.ai/learn/nptel/111101005/c731d0f674ee) (Video)
14. [L14-Measurable functions](https://invisiblenetwork.ai/learn/nptel/111101005/1634e48d4ded) (Video)
15. [L15-Properties of measurable functions](https://invisiblenetwork.ai/learn/nptel/111101005/d417c16e45d8) (Video)
16. [L16-Measurable functions on measure spaces](https://invisiblenetwork.ai/learn/nptel/111101005/6d6741a7bc09) (Video)
17. [L17-Integral of non negative simple measurable functions](https://invisiblenetwork.ai/learn/nptel/111101005/dc88ced43c52) (Video)
18. [L18-Properties of non negative simple measurable functions](https://invisiblenetwork.ai/learn/nptel/111101005/f56c2e8a9403) (Video)
19. [L19-Monotone convergence theorem & Fatou's Lemma](https://invisiblenetwork.ai/learn/nptel/111101005/8ace44e56d95) (Video)
20. [L20-Properties of Integral functions & Dominated Convergence Theorem](https://invisiblenetwork.ai/learn/nptel/111101005/b6655a786c8e) (Video)
21. [L21-Dominated Convergence Theorem and applications](https://invisiblenetwork.ai/learn/nptel/111101005/8fbf830639fe) (Video)
22. [L22-Lebesgue Integral and its properties](https://invisiblenetwork.ai/learn/nptel/111101005/1eaa119046ec) (Video)
23. [L23-Denseness of continuous function](https://invisiblenetwork.ai/learn/nptel/111101005/5f137540827c) (Video)
24. [L24-Product measures, an Introduction](https://invisiblenetwork.ai/learn/nptel/111101005/3bd1df4f2c2a) (Video)
25. [L25-Construction of Product Measure](https://invisiblenetwork.ai/learn/nptel/111101005/9188daa26426) (Video)
26. [L26-Computation of Product Measure-I](https://invisiblenetwork.ai/learn/nptel/111101005/d30d04c5e05f) (Video)
27. [L27-Computation of Product Measure-II](https://invisiblenetwork.ai/learn/nptel/111101005/0ad267a692bd) (Video)
28. [L28-Integration on Product spaces](https://invisiblenetwork.ai/learn/nptel/111101005/1bd99ae80e9d) (Video)
29. [L29-Fubini's Theorems](https://invisiblenetwork.ai/learn/nptel/111101005/5186a23fa8ab) (Video)
30. [L30-Lebesgue Measure and integral on R2](https://invisiblenetwork.ai/learn/nptel/111101005/6d1f4b687251) (Video)
31. [L31-Properties of Lebesgue Measure and integral on Rn](https://invisiblenetwork.ai/learn/nptel/111101005/e01ba8aa4aa6) (Video)
32. [L32-Lebesgue integral on R2](https://invisiblenetwork.ai/learn/nptel/111101005/bb85c7cca39f) (Video)
33. [L33-Integrating complex-valued functions](https://invisiblenetwork.ai/learn/nptel/111101005/07f08238b07d) (Video)
34. [L34-Lp - spaces](https://invisiblenetwork.ai/learn/nptel/111101005/2a6c0a585a0d) (Video)
35. [L35-L2(X,S,mue)](https://invisiblenetwork.ai/learn/nptel/111101005/85b3f6cc5a52) (Video)
36. [L36-Fundamental Theorem of calculas for Lebesgue Integral-I](https://invisiblenetwork.ai/learn/nptel/111101005/1d2cfe68304a) (Video)
37. [L37-Fundamental Theorem of calculus for Lebesgue Integral-II](https://invisiblenetwork.ai/learn/nptel/111101005/de32bc1d0323) (Video)
38. [L38-Absolutely continuous measures](https://invisiblenetwork.ai/learn/nptel/111101005/5e3d998da8cc) (Video)
39. [L39-Modes of convergence](https://invisiblenetwork.ai/learn/nptel/111101005/b8ba6de3d4ff) (Video)
40. [L40-Convergence in Measure](https://invisiblenetwork.ai/learn/nptel/111101005/ba6bc40c6ccf) (Video)