Measure Theory
Overview
Measure Theory formalises and generalises the notion of integration. It is fundamental to many areas
of mathematics and probability and has applications in other fields such as physics and economics.
Students will be introduced to Lebesgue measure and integration. Signed measures. Hahn-Jordan
decomposition. Radon-Nikodym derivative. Conditional expectation. Borel sets and standard Borel
spaces. Product measures. The Riesz representation theorem. The Krein-Milman theorem. The
Stone-Weierstrass theorem. The measure disintegration theorem. Ergodic theory.
Subject objectives
After completing this subject, students will:
- understand the fundamentals of measure theory and have an understanding of how these
underpin the use of mathematical concepts such as volume, area, and integration
- learn an advanced description of the basic notion of integration
- develop a perspective on the broader impact of measure theory in ergodic theory
- have the ability to pursue further studies in this and related areas
Coordinator
Gregory Hjorth.
Requisites & Pre-requisites
It is recommended that students have completed a third year subject in metric spaces, measure and
integral (equivalent to 620-311 [2008] Metric Spaces and
620-312 [2008] Linear Analysis).
Back to the 'Science subjects' list page