Math 525B
Real Analysis

Math 525B the second semester in the graduate Real Analysis sequencer.
The main topics are basic functional analysis, and examples of Banach
and other topological vector spaces which are important in
applications.
Textbook:
Folland: Real Analysis  Modern Techniques and Their Applications
(Second Edition, 1999).
List of Topics:
 Elements of Functional Analysis (Folland, Chapter 5)

Banach Spaces, HahnBanach Theorem and consequences, Baire
Category  Open Mapping  Closed Graph Theorem, Uniform
Boundedness Principle, Topological Vector Spaces (in particular
Frechet and weak topologies), Hilbert spaces.
 L^{p} spaces (mainly Folland, Chapter 6)

Basic inequalities and embeddings, L^{p} duality,
Convolutions, Rearrangement inequalities, Hardy inequalities,
Marcienkiewicz Interpolation Theorem, CalderonZygmund
decomposition and their application to the Poisson equation.
 Radon Measures

(Folland, 7.17.3)
 Basic Distribution Theory
 Haar Measures
Last modified: 2000/05/10
Marcel Oliver
(oliver@member.ams.org)