Math 241: Real analysis


	
This course develops measure theory and Lebesgue integration. This theory
is foundational for much of analysis and in particular for the mathematical
theory of probability. This course is a natural beginning part of a graduate
program in mathematics. Besides measure theory and integration (as in
Chapters 1--6, 11, and 12 in Royden's book, mentioned below), we include a
brief treatment of Fourier series and transforms, and the formulation of
probability theory in terms of measure theory. The main prerequisite is a
rigorous undergraduate course in real analysis. Students should have a
working knowledge of the concepts from undergraduate analysis and should
be used to writing proofs in analysis.