Measure and Integration (L.6)

Module code: G1070
Level 6
15 credits in autumn semester
Teaching method: Lecture
Assessment modes: Computer based exam, Coursework

This module provides a rigorous introduction to measure theory and Lebesgue integration. We will study measures and their properties, learn to construct measures from outer measures using Caratheodory's method, and construct the Lebesgue measure on the line. We will then develop the powerful concept of Lebesgue integral and make the use of it by mastering convergence theorems. The last part of the module gives an introduction to L^p spaces.

Module learning outcomes

  • A successful student should: know the concept and the properties of a sigma-additive measure;
  • understand how the concepts of integral and measure are related;
  • be able to state and apply central results of integration theory such as: monotone and dominated convergence theorems or theorems on parameter-dependent integrals;
  • know basic facts on L^p spaces.