Mathematics

Measure Theory with Applications (L.6)

Module code: G1070
Level 6
15 credits in autumn semester
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

This module gives you a rigorous introduction to measure theory and Lebesgue integration, as well as some of their applications.

You will study sigma-additive measures and their properties, learnimg to construct the Lebesgue measures from outer measures using Caratheodory's method.

You will then study the powerful concept of Lebesgue integral and the convergence theorems of the Lebesgue integration theory, as well as how to make use of them.

You’ll also be introduced to L^p spaces.

Module learning outcomes

• Systematically understand the concept and the properties of a sigma-additive measure
• Systematically understand how the concepts of integral and measure are related
• Be able to use and understand the convergence theorems of Lebesgue integration theory
• Know the basic facts on L^p spaces