Math 543 - Measure Theory

Instructor

Volker Runde

Office hours

TBA

Contents

Measure theory is the axiomatized study of areas and volumes. It is the basis of integration theory and provides the conceptual framework for probability.

This (non core) course is an introduction to measure theory. The following are the topics I will cover for sure:

1. Abstract measures: algebras and -algebras; measures; outer measures; Dynkin systems.
2. Integration: measurable functions; the measure theoretic integral; limit theorems; L^p-spaces.
3. Signed and complex measures: absolute continuity; the Radon-Nikodym theorem; Hahn and Lebesgue decomposition.
4. Product measures: Tonelli's theorem; Fubini's theorem; change of variables in R^N.

Depending on time available and on the participants' background, I may cover further topics on integration on locally compact spaces such as Riesz' representation theorem and the existence of Haar measure.

Prerequisites

Math 418

Textbooks

The required text is
D. L. Cohn, Measure Theory, Birkhäuser, 1985.

A recommended supplementary text is

P. R. Halmos, Measure Theory, Springer Verlag, 1974.

Grading

The grade will be based on regular homework assignments (50%) and a take home final (50%).