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General |
MATH 631 , Spring 2018: Notes and Summary
| Lecture | Date | What was covered | Notes | Textbook Section |
| 1 | Jan.25 | Review L^1 space and measure theory on R (I) | 4.4 | |
| 2 | Jan.30 |
Review L^1 space and measure theory on R(II) | Get HW1 | 4.4 |
| 3 | Feb. 1 | Littlewood's 3 principles: Measurable sets, Lusin Theorem, Egoroff theorem | ||
| 4 | Feb. 6 | Riesz-Markov Theorem (1). | Due HW1; Get HW2 | |
| 5 | Feb. 8 | Riesz-Markov (2) | ||
| 6 | Feb.13 | Riesz-Markov (3) | Due HW2; Get HW3 | |
| 7 | Feb.15 | Approximations by simple and step functions | ||
| 8 | Feb.20 | Riesz representation of the dual of Lp (1) | ||
| 9 | Feb.22 | Riesz representation of the dual of Lp (2) | Due HW3; Get HW4 | |
| 10 | Feb.27 | Differentiation of BV functions: Lebesgue theorem. (1) | ||
| 11 | Mar. 1 | Differentiation of BV functions: Lebesgue theorem. (2) | ||
| 12 | Mar. 6 | Differentiation of singular measures | Due HW4; Get HW5 | |
| 13 | Mar. 8 | Differentiation of absolutely continuous measures | ||
| 14 | Mar.13 | Topological and Metric Spaces. | ||
| 15 | Mar.15 | Separation axioms for topological spaces. The case of metric spaces. | Due HW5 | |
| - | Fri., Mar.16 | REVIEW SESSION | 11:00am-1:00pm | CSIC 4122 |
| - | Mar.19-23 | SPRING BREAK | NO CLASSES | |
| 16 | Mar.27 | MID TERM EXAM | ||
| 17 | Mar.29 | - | NO CLASS | |
| 18 | Apr. 3 | Normal spaces. Urysohn's Lemma | ||
| 19 | Apr. 5 | Urysohn's Metrizability Theorem | Due HW6 | |
| 20 | Apr.10 | Compact topological spaces. Product topology. | ||
| 21 | Apr.12 | Tychonoff's Theorem | ||
| 22 | Apr.17 | Compact Metric Spaces | ||
| 23 | Apr.19 | Partition of Unity. Premeasures. | Due HW7 | |
| 24 | Apr.24 | Measurable spaces and Spaces with measure. Preliminary results | ||
| 25 | Apr.26 | Outer Measures | ||
| 26 | May 1 | Caratheodory measurable sets. Caratheodory-Hahn theorem. | ||
| 27 | May 3 | Extension results. | ||
| 28 | May 8 | Integration of simple functions | ||
| 29 | May 10 | Integration in abstract spaces with measures. Miscellaneous results. | LAST CLASS | |
| - | Fri., May 11 | REVIEW SESSION | 11:00pm-1:00pm | CSIC 4122 |
| - | Sat., May 12 | FINAL EXAM | CSIC 4122 | 8:00am-10:00am |
