Betsy Stovall, Fall 2017: This is the first semester of the introductory graduate sequence in real analysis. We will cover measure theory, integration, L^p spaces, and some basic functional analysis (Hilbert and Banach spaces). There will be regular homework and two or three exams.
Continuation: Math 725 in the spring semester.
Sources: We will use Folland's Real Analysis.
Highly recommended are also Vol III-IV in the Princeton Lecture Series in Analysis, by Stein and Shakarchi (Vol III: Real analysis: Integration, measure theory and Hilbert spaces, Vol IV: Functional Analysis: Introduction to further topics in Analysis).