Schedule
We will switch between Axler and Royden. Axler sections are of the form
<number><letter>. Royden sections are of the form <number>.<number>.
| Week | Lectures | Sections | Comments | Student Reading |
|---|---|---|---|---|
| 1 | 8/27 8/29 | Axler 1A, 1B | Why Riemann Integral is Bad | Royden Chapter 1 |
| 2 | 9/03 9/05 | Royden 17.1, | General measure, signed measure (Hahn-Jordan) | Axler 2A |
| 3 | 9/10 9/12 | 17.3, 17.4 | Outermeasure, Caratheodory-Hahn: premeasure to measure. | Axler 2B |
| 4 | 9/17 9/19 | 18.1 | General Integration Theory | Axler 2C |
| 5 | 9/24 9/26 | 18.2, 18.3 | Simple Approximation, Egoroff, MON, DOM | Axler 2E, 3A |
| 6 | 10/01 10/03 | 2.6, 2.7, 3.3 | Nonmeasurable sets, Cantor Set and Function, Lusin | Axler 2D, 2E |
| 7 | 10/08 10/10 | 4A, 4B | Vitali covering, Lebesgue differentiation | Royden 6.1, 6.2 |
| 8 | —– 10/17 | Midterm | Fall Break 10/14-10-15 | |
| 9 | 10/22 10/24 | 17.2, 17.5 | Radon-Nikodym theorem | Axler 4B |
| 10 | 10/29 10/31 | 7.1, 20.1 | FTC (from Rudin), Product Measures | Axler 5A |
| 11 | 11/05 11/07 | 20.2, 5.2 | Fubini-Tonelli, Convergence in Measure | Axler 5B, 5C |
| 12 | 11/12 11/14 | Axler 6A,6B, 6C | Metric Spaces, Vector Spaces, Norms | Royden 9.1-9.6 |
| 13 | 11/19 11/21 | 6C, 6D | Hahn-Banach, Baire Category | Royden 10.1-10.3 |
| 14 | 11/26 —– | 6E | Baire Category, Thanksgiving | Axler 7A |
| 15 | 12/03 12/05 | 7A, 7B | Holder, Young, Minkowski, completeness, Riesz | Axler 7B |
| 17 | 12/10 12/12 | Makeup | Last day of classes Dec 13 | |
| 17 | 12/16 | Final Exam | Monday December 16 |