Course image MAT2164 Measure Theory and Integration
Trim I

This module aims at studying the abstract theory of measures and Lebesgue Integration. A measure is a generalization of the concepts of length, area, and volume in finite-dimensional Euclidean spaces. The Lebesgue integral is a generalization of the Riemann integral to a large class of functions.

Topics covered in this module are the abstract theory of measures on sigma-algebras, measurable functions, essential properties of the Lebesgue measure, fundamental theorems of the Lebesgue integral, the connection between the Riemann and Lebesgue integrals, product spaces, and Fubini and Tonelli Theorems. The module will deal with these topics at a basic level appropriate for undergraduate students in Applied Mathematics.

The knowledge of the theory of measure and integration is essential for the study of several advanced topics in Functional Analysis, Partial Differential Equations, and many other areas of Mathematics. In particular, the theory of measure and integration is vital to the study of Probability and Stochastic Processes.