Measure and Integration


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Module Overview: Measure and Integration

This module covers the following topics:

  • Concrete examples (Riemann and Lebesgue)
  • Abstract theory - convergence theorems
  • Signed, product and Radon measures
  • Fractal sets and Hausdorff dimension
Weekly Preparation

Students should read and study the lecture notes prior to the lecture time and come prepared to discuss and ask questions about topics covered in the notes.

  • Undergraduate analysis: Sequences, series, pointwise and uniform convergence
  • Metric space topology: At least in R^d, continuity of functions, open, closed and compact sets
  • Countable sets

This module is assessed in two assignments, one in mid November and the other in mid December. Each will consist of around three questions.