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.
Teaching and assessment
We’re currently reviewing teaching and assessment of our modules in light of the COVID-19 situation. We’ll publish the latest information as soon as possible.
Contact hours and workload
This module is approximately 150 hours of work. This breaks down into about 33 hours of contact time and about 117 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.
This module is running in the academic year 2020/21. 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.
This module is offered on the following courses: