MAT5213
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Introduction to abstract measure theory and integration.
Topics List
| Week | Topic | Sections from Rudin's Real and Complex Analysis | Prerequisites |
|---|---|---|---|
| 1 | Abstract integration | Chapter 1 | Real Analysis I |
| 2-3 | Positive Borel measures | Chapter 2 | |
| 4-5 | Lp spaces | Chapter 3 | |
| 7-9 | Hilbert spaces | Chapter 4 | |
| 10-12 | Complex measures | Chapter 5 | |
| 13-14 | The Radon-Nikodym theorem and its consequences | Chapter 6 | |
| 15-16 | Product spaces and Fubini's theorem | Chapter 7 |
