From Department of Mathematics at UTSA
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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