| Week 1 |
Review of measure theory: Caratheodory and Lebesgue measure |
| Week 2 |
Integration, MON, DOM and other convergence theorems, Radon-Nikodym. Probability and Random variables. |
| Week 3 |
Expectation, L^p spaces, Chebyshev, Markov. Jensen’s inequality. |
| Week 4 |
Hilbert spaces and Radon-Nikodym. |
| Week 5 |
Basic probability theory. Chapter 8 from Le Gall. |
| Week 6 |
Product spaces, Fubini’s theorem, Independence. |
| Week 7 |
Infinite products, Borel-Cantelli lemma. |
| Week 8 |
Weak and Strong Law of large numbers |
| Week 9 |
Spring Break (Mar 8 - Mar 16) |
| Week 10 |
MIDTERM Mar 20. More on the Strong Law |
| Week 11 |
Fourier Transforms redux, Central Limit Theorem |
| Week 12 |
Other proofs of the CLT |
| Week 13 |
Conditional probability and expectation |
| Week 14 |
Martingales |
| Week 15 |
|
| Final |
May 9, 9-12 |