Topics
# Topics Covered in Math 504

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We will cover as much of the text
*Real Analysis, *
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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