Measure and Integration (850G1)
15 credits, Level 7 (Masters)
In this module, you cover:
- countably additive measures, sigma-algebras, Borel sets, measure spaces
- outer measures and Caratheodory's construction of measures
- construction and properties of Lebesgue measure in Euclidean spaces
- measurable and integrable functions, Lebesgue integration theory on measure spaces, L^p spaces and their properties
- convergence theorems: monotone convergence, dominated convergence, Fatou's lemma
- application of limit theorems to continuity and differentiability of integrals depending on a parameter
- properties of finite measure spaces and probability theory.
20%: Coursework (Problem Set)
80%: Examination (Unseen examination)
Contact hours and workload
This module is 150 hours of work. This breaks down into 33 hours of contact time and 117 hours of independent study.
This module is running in the academic year 2019/20. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.