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Required Text: Measure, Integration & Real Analysis (2020) by Sheldon Axler
(Cheap from Springer/bookstores, free at https://measure.axler.net/)
| Schedule: |
| Weeks 1-2 |
Preliminaries: Cardinality, transfinite induction; review of metric spaces
Start measure theory
Handouts:
Assignments:
- Read Chapter 1 (we won't be discussing this much)
- 1A/7,8 (these are similar), 13 (these are all nice 431-level problems)
- 1B/5 (I think I'm going to have you hand this one in, date TBD)
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| Weeks 3-4 |
Measure spaces, Lebegue measure, Lebesgue integral
Here are the handouts I gave ou in class (but updated):
Assignments:
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| Week 5-6 |
Integration; limit theorems
Assignments:
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| Weeks 7-9 |
Assignments:
- Chapters 7 and 9, but only for real-valued measures
- Assignment 5 (problems due Oct 28)
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| The rest |
Assignments:
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