# Measure Theory

- Institution: IIT Bombay
- Department: Mathematics
- Teacher: Prof. Inder Kumar Rana
- Level: Graduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111101100)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111101100)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This is a course on the concepts of Measure and Integration. Normally, this is a core course for M,.Sc. Mathematics and Statistics students. The concepts find applications in advance Analysis Courses, Signal Processing, Financial Mathematics courses.

INTENDED AUDIENCE : B.Tech Dual degree in Electrical, M.Sc. Physics, mathematics

PREREQUISITES : Basic Course in Real Analysis

## Lectures

1. [Lecture 1A: Introduction, Extended Real Numbers](https://invisiblenetwork.ai/learn/nptel/111101100/65d9586958a0) (YouTube)
2. [Lecture 1B: Introduction, Extended Real Numbers](https://invisiblenetwork.ai/learn/nptel/111101100/d443f319acaf) (YouTube)
3. [Lecture 2A: Algebra and Sigma Algebra of Subsets of a Set](https://invisiblenetwork.ai/learn/nptel/111101100/78df631c81f7) (YouTube)
4. [Lecture 2B: Algebra and Sigma Algebra of Subsets of a Set](https://invisiblenetwork.ai/learn/nptel/111101100/27a3651e5feb) (YouTube)
5. [Lecture 3A: Sigma Algebra generated by a Class](https://invisiblenetwork.ai/learn/nptel/111101100/59882290a46f) (YouTube)
6. [Lecture 3B: Sigma Algebra generated by a Class](https://invisiblenetwork.ai/learn/nptel/111101100/f689a3d57853) (YouTube)
7. [Lecture 4A: Monotone Class](https://invisiblenetwork.ai/learn/nptel/111101100/19ed568b1dba) (YouTube)
8. [Lecture 4B: Monotone Class](https://invisiblenetwork.ai/learn/nptel/111101100/781807a77242) (YouTube)
9. [Lecture 5A: Set Functions](https://invisiblenetwork.ai/learn/nptel/111101100/c5ceb35b3aa0) (YouTube)
10. [Lecture 5B: Set Functions](https://invisiblenetwork.ai/learn/nptel/111101100/380596c3189d) (YouTube)
11. [Lecture 6A: The Length Function and its Properties](https://invisiblenetwork.ai/learn/nptel/111101100/84810bd786a5) (YouTube)
12. [Lecture 6B: The Length Function and its Properties](https://invisiblenetwork.ai/learn/nptel/111101100/4fe5d285fb2f) (YouTube)
13. [Lecture 7A: Countably Additive Set Functions on Intervals](https://invisiblenetwork.ai/learn/nptel/111101100/91f126cd172c) (YouTube)
14. [Lecture 7B: Countably Additive Set Functions on Intervals](https://invisiblenetwork.ai/learn/nptel/111101100/b3ae7bab6580) (YouTube)
15. [Lecture 8A: Uniqueness Problem for Measure](https://invisiblenetwork.ai/learn/nptel/111101100/7ae794bcb302) (YouTube)
16. [Lecture 8B: Uniqueness Problem for Measure](https://invisiblenetwork.ai/learn/nptel/111101100/6b4cf729d21d) (YouTube)
17. [Lecture 9A: Extension of Measure](https://invisiblenetwork.ai/learn/nptel/111101100/60f1ed5ab711) (YouTube)
18. [Lecture 9B: Extension of Measure](https://invisiblenetwork.ai/learn/nptel/111101100/237e0c0a8b45) (YouTube)
19. [Lecture 10A: Outer Measure and its Properties](https://invisiblenetwork.ai/learn/nptel/111101100/8beee92e1e12) (YouTube)
20. [Lecture 10B: Outer Measure and its Properties](https://invisiblenetwork.ai/learn/nptel/111101100/72fedcea090e) (YouTube)
21. [Lecture 11A: Measurable Sets](https://invisiblenetwork.ai/learn/nptel/111101100/f57df49ee7c3) (YouTube)
22. [Lecture 11B: Measurable Sets](https://invisiblenetwork.ai/learn/nptel/111101100/843e2cb8fa2b) (YouTube)
23. [Lecture 12A: Lebesgue Measure and its Properties](https://invisiblenetwork.ai/learn/nptel/111101100/c868dc152c87) (YouTube)
24. [Lecture 12B: Lebesgue Measure and its Properties](https://invisiblenetwork.ai/learn/nptel/111101100/f7caef8f5ef0) (YouTube)
25. [Lecture 13A: Characterization of Lebesgue Measurable Sets](https://invisiblenetwork.ai/learn/nptel/111101100/cbe2139406f8) (YouTube)
26. [Lecture 13B: Characterization of Lebesgue Measurable Sets](https://invisiblenetwork.ai/learn/nptel/111101100/d7f1ebe13f23) (YouTube)
27. [Lecture 14A: Measurable Functions](https://invisiblenetwork.ai/learn/nptel/111101100/b7fe3c64cbb6) (YouTube)
28. [Lecture 14B: Measurable Functions](https://invisiblenetwork.ai/learn/nptel/111101100/19ddd77566b2) (YouTube)
29. [Lecture 15A: Properties of Measurable Functions](https://invisiblenetwork.ai/learn/nptel/111101100/b5c031b059eb) (YouTube)
30. [Lecture 15B: Properties of Measurable Functions](https://invisiblenetwork.ai/learn/nptel/111101100/118d426cf0f6) (YouTube)
31. [Lecture 16A: Measurable Functions on Measure Spaces](https://invisiblenetwork.ai/learn/nptel/111101100/a36b70dc2dfe) (YouTube)
32. [Lecture 16B: Measurable Functions on Measure Spaces](https://invisiblenetwork.ai/learn/nptel/111101100/eccff428459a) (YouTube)
33. [Lecture 17A: Integral of Nonnegative Simple Measurable Functions](https://invisiblenetwork.ai/learn/nptel/111101100/60387fa92e0e) (YouTube)
34. [Lecture 17B: Integral of Nonnegative Simple Measurable Functions](https://invisiblenetwork.ai/learn/nptel/111101100/b63340886b1f) (YouTube)
35. [Lecture 18A: Properties of Nonnegative Simple Measurable Functions](https://invisiblenetwork.ai/learn/nptel/111101100/709bf5034f9a) (YouTube)
36. [Lecture 18B: Properties of Nonnegative Simple Measurable Functions](https://invisiblenetwork.ai/learn/nptel/111101100/07063ed4a309) (YouTube)
37. [Lecture 19A: Monotone Convergence Theorem and Fatou's Lemma](https://invisiblenetwork.ai/learn/nptel/111101100/b0c4c8ce6a12) (YouTube)
38. [Lecture 19B: Monotone Convergence Theorem and Fatou's Lemma](https://invisiblenetwork.ai/learn/nptel/111101100/785c34dd3d18) (YouTube)
39. [Lecture 20A: Properties of Integrable Functions and Dominated Convergence Theorem](https://invisiblenetwork.ai/learn/nptel/111101100/a8182e7f10ee) (YouTube)
40. [Lecture 20B: Properties of Integrable Functions and Dominated Convergence Theorem](https://invisiblenetwork.ai/learn/nptel/111101100/d0893f9d780e) (YouTube)
41. [Lecture 21A: Dominated Convergence Theorem and Applications](https://invisiblenetwork.ai/learn/nptel/111101100/97a57ae9f2e4) (YouTube)
42. [Lecture 21B: Dominated Convergence Theorem and Applications](https://invisiblenetwork.ai/learn/nptel/111101100/2bb5af5971f9) (YouTube)
43. [Lecture 22A: Lebesgue Integral and its Properties](https://invisiblenetwork.ai/learn/nptel/111101100/576cf0d1f6eb) (YouTube)
44. [Lecture 22B: Lebesgue Integral and its Properties](https://invisiblenetwork.ai/learn/nptel/111101100/71226520be0a) (YouTube)
45. [Lecture 23A: Product Measure, an Introduction](https://invisiblenetwork.ai/learn/nptel/111101100/3000d55681da) (YouTube)
46. [Lecture 23B: Product Measure, an Introduction](https://invisiblenetwork.ai/learn/nptel/111101100/0e0930bea987) (YouTube)
47. [Lecture 24A: Construction of Product Measures](https://invisiblenetwork.ai/learn/nptel/111101100/9204fdca2f97) (YouTube)
48. [Lecture 24B: Construction of Product Measures](https://invisiblenetwork.ai/learn/nptel/111101100/759804ba222f) (YouTube)
49. [Lecture 25A: Computation of Product Measure - I](https://invisiblenetwork.ai/learn/nptel/111101100/d16d50570843) (YouTube)
50. [Lecture 25B: Computation of Product Measure - I](https://invisiblenetwork.ai/learn/nptel/111101100/ae6e7b2c2d24) (YouTube)
51. [Lecture 26A: Computation of Product Measure - II](https://invisiblenetwork.ai/learn/nptel/111101100/34d818bdedec) (YouTube)
52. [Lecture 26B: Computation of Product Measure - II](https://invisiblenetwork.ai/learn/nptel/111101100/553c20310c9f) (YouTube)
53. [Lecture 27A: Integration on Product Spaces](https://invisiblenetwork.ai/learn/nptel/111101100/d56aa65c7fc3) (YouTube)
54. [Lecture 27B: Integration on Product Spaces](https://invisiblenetwork.ai/learn/nptel/111101100/5a04385f64e3) (YouTube)
55. [Lecture 28A: Fubini's Theorems](https://invisiblenetwork.ai/learn/nptel/111101100/14d551fa3835) (YouTube)
56. [Lecture 28B: Fubini's Theorems](https://invisiblenetwork.ai/learn/nptel/111101100/65d429bc7df9) (YouTube)
57. [Lecture 29A: Lebesgue Measure and Integral on R2](https://invisiblenetwork.ai/learn/nptel/111101100/00abb368e77b) (YouTube)
58. [Lecture 29B: Lebesgue Measure and Integral on R2](https://invisiblenetwork.ai/learn/nptel/111101100/eff100e412a9) (YouTube)
59. [Lecture 30A: Properties of Lebesgue Measure on R2](https://invisiblenetwork.ai/learn/nptel/111101100/1452bfebd5b3) (YouTube)
60. [Lecture 30B: Properties of Lebesgue Measure on R2](https://invisiblenetwork.ai/learn/nptel/111101100/cf4a605901bc) (YouTube)
61. [Lecture 31A: Lebesgue Integral on R2](https://invisiblenetwork.ai/learn/nptel/111101100/c14c5496cc8c) (YouTube)
62. [Lecture 31B: Lebesgue Integral on R2](https://invisiblenetwork.ai/learn/nptel/111101100/2fdd8cefa815) (YouTube)