| Meetings: MWF 8:50-9:40, B131 Van Vleck |
| Instructor: Timo Seppäläinen |
| Office: 419 Van Vleck, office hours after class or by appointment |
| Phone: 263-2812 |
| E-mail: seppalai@math.wisc.edu |
| Course homepage: http://www.math.wisc.edu/~seppalai/courses/629/629home.html |
Prerequisites: Some rigorous analysis, or ability to learn it as we proceed.
Textbook: Real Analysis by Gerald B. Folland, first or second edition.
This course is an introduction to measure theory and some related notions from probability theory. We will cover the basics of sigma algebras and measures, Lebesgue integration, the basic convergence theorems for integrals, types of convergence for functions, product measures, L^p spaces, and the Radon-Nikodym theorem. On the probability side, this means covering probability spaces, random variables, expectations, the convergence of expectations and random variables, and possibly conditional expectations. The relevant parts from the book are Chapters 1 and 2, the Lebesgue-Radon-Nikodym theorem from Chapter 3, and L^p spaces from Chapter 6.
Course grades will be based on some homework and take-home exams.