Topics Covered in Math 504
We will cover as much of the text
by Stein and Shakarchi, as we have time for.
We will cover Chapters 1 through 3 more or less entirely, perhaps
omitting some starred sections. We will extract selected
results from Chapters 4 and 5, but we do not want to overlap too much
with Math 502. We will do as much of Chapters 6 and 7 as we can.
- Chapter 1. Measure Theory (Lebesgue measure)
- Chapter 2. Integration Theory (with respect to Lebesgue measure)
- Chapter 3. Differentiation and Integration
- Chapter 4. Hilbert Spaces: an Introduction
- Chapter 5. Hilbert Spaces: Several Examples
- Chapter 6. Abstract Measure and Integration Theory
- Chapter 7. Hausdorff Measures and Fractals
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