MATH 6210: Measure Theory and Lebesgue Integration (Fall 2012)

Instructor: John Smillie

Prerequisites: undergraduate analysis and linear algebra as taught in MATH 4130 and 4310.

Texts: We will use the books The Elements of Integration and Lebesgue Measure by Robert Bartles and A Terse Introduction to Lebesgue Integration by John Franks.

The Riemann integral familiar from undergraduate calculus has poor convergence properties and does not behave well in higher dimensions. A much more convenient and flexible theory of integration, based on the notion of a countably additive measure, was developed by Henri Lebesgue. In this course we develop Lebesgue’s theory from the ground up.

This course is designed for students who need the theory for applications to fields including probability, statistics, economics, functional analysis and PDEs.