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Introduction to abstract measure theory and integration. | Introduction to abstract measure theory and integration. | ||
| + | |||
| + | ==Topics List== | ||
| + | {| class="wikitable sortable" | ||
| + | ! 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 | ||
| + | || | ||
| + | |} | ||
Latest revision as of 21:06, 18 March 2023
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 |
