MATH0017 Measure Theory

Term 1 2025/26

University College London

Lecturer: Aleksander Doan ([email protected])

Teaching assistants: Jun Cheng, William Magarey

Syllabus: https://www.ucl.ac.uk/maths/sites/maths/files/math0017.pdf

Course materials: Lecture notes, homework, quizzes, past exams on Moodle

Final mark: 90% Exam, 10% Coursework

Coursework: Weekly homework problems, presentations of solutions at weekly problem sessions with the lecturer and teaching assistants

Prerequisites

To follow the course, you must ****be familiar with basic set theory, supremum and infimum, limsup and liminf, and limits. Many freely available analysis textbooks cover these topics, for example Lectures 1—9 of the MIT lecture notes by Dote and Rodriguez and I strongly recommend reviewing this material if you don’t remember parts of it. Below is a more detailed list of prerequisites, but the four topics listed above are essential.

• Basic logic and quantifiers
• Induction
• Sets, subsets, power set of a set
• Operations on sets: union, intersection, difference, complement, de Morgan’s laws
• Maps between sets: domain, codomain, image, preimage, injective\surjective\bijective maps
• Countable and uncountable sets, cardinality
• Cartesian product of sets