The theory of integration in abstract and Euclidean spaces, and an introduction to the basic ideas of functional analysis. Math 5051-5052 forms the basis for the Ph.D. qualifying exam in analysis. Prereq: Math 417-418.
Topics we will cover:
Set theory
Topology
Banach spaces
C(X) spaces
Weak* topologies
Measure theory
There is no textbook. We will follow a set of notes which I will distribute periodically.