Measure and Integration (L.7) (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 (Portfolio, Problem set)
80%: Examination (Computer-based examination)
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 2021/22. We also plan to offer it in future academic years. However, we are constantly looking to improve and enhance our courses. There may be changes to modules in response to student demand or feedback, changes to staff expertise or updates to our curriculum. We may also need to make changes in response to COVID-19. We’ll make sure to let our applicants know of material changes to modules at the earliest opportunity.
This module is offered on the following courses: