This is an online course which is given at the University of Freiburg.

Requirements: If you want to have a Studienleistung, you must hand in parts of the exercises. Please contact Peter Pfaffelhuber if you want to do so.

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.

Exercises: You can find the exercises as part of the manuscript.