Measure Theory

Lecturer: A.L. Pinchuck

Prerequisites

Real analysis (M3.3) or an equivalent course is a necessary prerequisite for this course and knowledge of metric spaces would be advantageous.

Description

Measure theory is the study of measure and integration. In this course we begin by looking at the shortcomings of Riemann integration as a motivation for a better theory of integration. This leads to the definition of a measure and a measure space. Measure theory can essentially be divided into the study of integration and the related study of measurable functions. Measure theory has applications in probability theory, ergodic theory, functional analysis and other areas. Important topics include the Lebesgue measure on the real numbers, the Lebesgue integral, properties of measurable functions, Lp spaces and a comparison between the theories of Riemann integration and Lebesgue integration.

Textbook

None prescribed. Complete course notes will be provided.

Tutorials

One tutorial per week.

Tests/Exams

Two tests and one final examination.

Last Modified: Fri, 15 Jul 2011 14:57:10 SAST