Measure and Integration

Content

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Description

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

Weeks 1, 2, 3, 4: Friday 10.00am-12.00pm. Weeks 5, 6, 7, 8, 9, 10: Wednesday 3.30-5.30pm.

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.

Prerequisites

• 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

Assessment

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