MA321      Half Unit
Measure Theoretic Probability

This information is for the 2025/26 session.

Course Convenor

Prof Graham Brightwell

Availability

This course is available on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics, Erasmus Reciprocal Programme of Study and Exchange Programme for Students from University of California, Berkeley. This course is freely available as an outside option to students on other programmes where regulations permit. It does not require permission. This course is available with permission to General Course students.

Requisites

Pre-requisites:

Students must have completed MA203 before taking this course.

Course content

This is a first course in measure-theoretic probability. It covers the following topics. Abstract probability spaces: sample spaces, sigma-algebras, probability measures, examples. Borel sigma-algebra, Lebesgue measure. Random variables: distribution functions, discrete and absolutely continuous distributions, examples. Expectation and the Lebesgue integral: convergence theorems and properties. Different modes of convergence of random variables. Conditional expectation: definition, properties, examples. Changes of probability measure, Bayes' theorem.

Teaching

20 hours of lectures and 10 hours of classes in the Autumn Term.

Formative assessment

Written answers to set problems will be expected on a weekly basis. 

Indicative reading

Comprehensive lecture notes will be provided.

The following books may prove useful: 

D Williams, Probability with Martingales.

J. Jacod & P. Protter, Probability Essentials; A. Klenke Probability Theory. A Comprehensive Course

Assessment

Exam (100%), duration: 120 Minutes in the Spring exam period


Key facts

Department: Mathematics

Course Study Period: Autumn Term

Unit value: Half unit

FHEQ Level: Level 6

CEFR Level: Null

Total students 2024/25: 23

Average class size 2024/25: 12

Capped 2024/25: No
Guidelines for interpreting course guide information

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

Personal development skills

  • Self-management
  • Problem solving
  • Communication
  • Application of numeracy skills
  • Specialist skills