Math 611 — Fall 2001 Real Analysis

This is the core course in real analysis. We will cover basic measure theory and abstract integration, the Riesz representation theorem, construction of Lebesgue measure, Fubini's theorem, the Radon-Nikodym theorem, differentiation of measures, basic functional analysis (Banach spaces, Lp spaces, the Hahn-Banach theorem, the Banach-Steinhaus theorem, the Open Mapping Theorem), convolution, and the Fourier transform. The text is Real and Complex Analysis by Walter Rudin.

Heads up: this course will be homework heavy. It, with the other core classes, takes the place of a qualifying exam, and so you should expect to work very hard (and learn a lot) in this course.