Part II Analysis of Functions, Lent 2026

This page contains information for students taking my lectures on Analyis of Functions in Lent 2025. The best way to contact me outside lectures is by email: pv270@dpmms.cam.ac.uk. (I do not monitor Moodle.)

Lecture Notes. (Last updated: 5 February 2026.) The notes will be updated in the course of the term. Please check back, and see the changelog below.

Example sheets:

• First example sheet. (4 February 2026.)

Lecture recordings are available via Panopto. However, I expect that most students will find the notes more useful.

Changelogs

Notes

• Version of 22 January 2026: Contains most of the material related to measure theory.
• Version of 26 January 2026: Added the Riesz representation theorem.
• Version of 4 February 2026: Added section on L^p spaces.
• Version of 5 February 2026: Added section on convolution.

Example Sheet 1

• Version of 4 February 2026: Typos corrected in questions 2, 4, 8 and 10. Hint added to question 6.