# Measure Theory

- Institution: IISc Bangalore
- Department: Mathematics
- Teacher: Prof. E. K. Narayanan
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111108135)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111108135)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Review of Riemann integration and introduction to sigma algebras](https://invisiblenetwork.ai/learn/nptel/111108135/e072102984a3) (Video)
2. [Sigma algebras and measurability](https://invisiblenetwork.ai/learn/nptel/111108135/4972b2540126) (Video)
3. [Measurable functions and approximation by simple functions](https://invisiblenetwork.ai/learn/nptel/111108135/69c09d251dbd) (Video)
4. [Properties of countably additive measures](https://invisiblenetwork.ai/learn/nptel/111108135/65712d7d4dde) (Video)
5. [Integration of positive measurable functions](https://invisiblenetwork.ai/learn/nptel/111108135/85fd25aa4018) (Video)
6. [Some properties of integrals of positive simple functions](https://invisiblenetwork.ai/learn/nptel/111108135/0a245df35cd8) (Video)
7. [Monotone convergence theorem and Fatou's lemma](https://invisiblenetwork.ai/learn/nptel/111108135/1d2c03c46f05) (Video)
8. [Integration of complex valued measurable functions](https://invisiblenetwork.ai/learn/nptel/111108135/5980999374a2) (Video)
9. [Dominated convergence theorem](https://invisiblenetwork.ai/learn/nptel/111108135/f189b3585847) (Video)
10. [Sets of measure zero and completion](https://invisiblenetwork.ai/learn/nptel/111108135/458583544132) (Video)
11. [Consequences of MCT, Fatou's lemma and DCT](https://invisiblenetwork.ai/learn/nptel/111108135/0314c8988b8a) (Video)
12. [Rectangles in R^n and some properties](https://invisiblenetwork.ai/learn/nptel/111108135/66e4951cdd35) (Video)
13. [Outer measure on R^n](https://invisiblenetwork.ai/learn/nptel/111108135/d1223893cb8c) (Video)
14. [Properties of outer measure on R^n](https://invisiblenetwork.ai/learn/nptel/111108135/a36bcb948a5f) (Video)
15. [Lebesgue measurable sets and Lebesgue measure on R^n](https://invisiblenetwork.ai/learn/nptel/111108135/6cc86ca49242) (Video)
16. [Lebesgue sigma algebra](https://invisiblenetwork.ai/learn/nptel/111108135/14bf920d1f58) (Video)
17. [Lebesgue measure.](https://invisiblenetwork.ai/learn/nptel/111108135/f1f4673100af) (Video)
18. [Fine properties of measurable sets](https://invisiblenetwork.ai/learn/nptel/111108135/c139c1a950e3) (Video)
19. [Invariance properties of Lebesgue measure](https://invisiblenetwork.ai/learn/nptel/111108135/f3046fda4826) (Video)
20. [Non measurable set](https://invisiblenetwork.ai/learn/nptel/111108135/bcbee609e3c1) (Video)
21. [Measurable functions.](https://invisiblenetwork.ai/learn/nptel/111108135/a786e28036ff) (Video)
22. [Riemann and Lebesgue integrals](https://invisiblenetwork.ai/learn/nptel/111108135/56298fc73ea7) (Video)
23. [Locally compact Hausdorff spaces](https://invisiblenetwork.ai/learn/nptel/111108135/d874a8a1193c) (Video)
24. [Riesz representation theorem](https://invisiblenetwork.ai/learn/nptel/111108135/797228dd0d84) (Video)
25. [Positive Borel measures](https://invisiblenetwork.ai/learn/nptel/111108135/37cb75d8124e) (Video)
26. [Lebesgue measure via Riesz representation theorem](https://invisiblenetwork.ai/learn/nptel/111108135/27038fc8b0e7) (Video)
27. [Construction of Lebesgue measure](https://invisiblenetwork.ai/learn/nptel/111108135/00e486e0006f) (Video)
28. [Invariance properties of Lebesgue measure.](https://invisiblenetwork.ai/learn/nptel/111108135/57c267bb3378) (Video)
29. [Linear transformations and Lebesgue measure](https://invisiblenetwork.ai/learn/nptel/111108135/eafca6543df9) (Video)
30. [Cantor set](https://invisiblenetwork.ai/learn/nptel/111108135/6dd003e36a2c) (Video)
31. [Cantor function](https://invisiblenetwork.ai/learn/nptel/111108135/b657ac21fdae) (Video)
32. [Lebesgue set which is not Borel](https://invisiblenetwork.ai/learn/nptel/111108135/eeaf7c8f11a0) (Video)
33. [L^p spaces](https://invisiblenetwork.ai/learn/nptel/111108135/f388a2ca8a7f) (Video)
34. [L^p norm](https://invisiblenetwork.ai/learn/nptel/111108135/cd8a9563443e) (Video)
35. [Completeness of L^p](https://invisiblenetwork.ai/learn/nptel/111108135/8b9443a216ed) (Video)
36. [Properties of L^p spaces](https://invisiblenetwork.ai/learn/nptel/111108135/8eb0a36e14de) (Video)
37. [Examples of L^p spaces](https://invisiblenetwork.ai/learn/nptel/111108135/1edfefb42161) (Video)
38. [Product sigma algebra](https://invisiblenetwork.ai/learn/nptel/111108135/9a6805ba3c4f) (Video)
39. [Product measures I](https://invisiblenetwork.ai/learn/nptel/111108135/8da6f4f9787c) (Video)
40. [Product measures II](https://invisiblenetwork.ai/learn/nptel/111108135/ecdca43b98a4) (Video)
41. [Fubini's theorem I](https://invisiblenetwork.ai/learn/nptel/111108135/8aac568cddc0) (Video)
42. [Fubini's theorem II](https://invisiblenetwork.ai/learn/nptel/111108135/06f49cffa4c3) (Video)
43. [Completeness of product measures](https://invisiblenetwork.ai/learn/nptel/111108135/d407ffc5a604) (Video)
44. [Polar coordinates](https://invisiblenetwork.ai/learn/nptel/111108135/f7608c759e60) (Video)
45. [Applications of Fubini's theorem](https://invisiblenetwork.ai/learn/nptel/111108135/280e06c5d737) (Video)
46. [Complex measures I](https://invisiblenetwork.ai/learn/nptel/111108135/bf85821a172d) (Video)
47. [Complex measures II](https://invisiblenetwork.ai/learn/nptel/111108135/b1eba8dea5a9) (Video)
48. [Absolutely continuous measures](https://invisiblenetwork.ai/learn/nptel/111108135/a05b155e5a69) (Video)
49. [L^2 space](https://invisiblenetwork.ai/learn/nptel/111108135/a9fcc2b08f47) (Video)
50. [Continuous linear functionals](https://invisiblenetwork.ai/learn/nptel/111108135/1dbe95ca373b) (Video)
51. [Radon-Nikodym theorem I](https://invisiblenetwork.ai/learn/nptel/111108135/b2297f231c6f) (Video)
52. [Radon Nikodym theorem II](https://invisiblenetwork.ai/learn/nptel/111108135/743980c49383) (Video)
53. [Consequences of Radon-Nikodym theorem I](https://invisiblenetwork.ai/learn/nptel/111108135/85767df63853) (Video)
54. [Consequences of Radon-Nikodym theorem II](https://invisiblenetwork.ai/learn/nptel/111108135/b84cad1421f8) (Video)
55. [Continuous linear functionals on L^p spaces I](https://invisiblenetwork.ai/learn/nptel/111108135/a6fb52160b89) (Video)
56. [Continuous linear functionals on L^p spaces II](https://invisiblenetwork.ai/learn/nptel/111108135/4442af0bf8f2) (Video)
57. [Riesz representation theorem I](https://invisiblenetwork.ai/learn/nptel/111108135/1b9f25226272) (Video)
58. [Riesz representation theorem II](https://invisiblenetwork.ai/learn/nptel/111108135/855aa6e3886f) (Video)
59. [Hardy-Littlewood maximal function](https://invisiblenetwork.ai/learn/nptel/111108135/6ec25ae2a5fd) (Video)
60. [Lebesgue differentiation theorem](https://invisiblenetwork.ai/learn/nptel/111108135/a811726af6c9) (Video)
61. [Absolutely continuous functions I](https://invisiblenetwork.ai/learn/nptel/111108135/365e421f1194) (Video)
62. [Absolutely continuous functions II](https://invisiblenetwork.ai/learn/nptel/111108135/87efb5b6ab69) (Video)
63. [Live Session 09-03-2021](https://invisiblenetwork.ai/learn/nptel/111108135/e072102984a3-2) (Video)
64. [Live Session 30-03-2021](https://invisiblenetwork.ai/learn/nptel/111108135/4972b2540126-2) (Video)