This is a hybrid course which is given at the University of Freiburg. Lectures will be given with videos (see below). Tutorials take place in person, Tuesdays, 14:15–15:45, in seminar room 232 (Ernst-Zermelo-Str. 1), starting 20th of October, 2026. There is no tutorial on 22nd of December, 2026.

Requirements for the Prüfungsleistung: You must pass the oral exam.

Content: The course covers the material which is usually needed in order to dive into measure theoretic aspects of probability theory. Usually, in basic lectures on probability (e.g. taught in Freiburg as Stochastik 1 in the 3rd semester), no measure theory is needed. Rather, the lecture in Analysis 3 covers measure theory. However, in case you want to specialize in probability theory and did not attend Analysis 3, this course is for you.

Prerequisites: You need to know fundamentals of mathematics, such as sets, functions etc. The course requires some knowledge in topology, but tries to recall all explanations in this field.

Manuscript: The current version is here.

Videos: Below you find links to all Videos, or you look at the playlist . A collection of all slides is here.

Exercise sheets: The homeworks are handed out on Tuesdays, and can be handed in by Monday, 10:00. It is allowed to hand in solutions with one partner, i.e. two students hand in one solution.