**Prerequisites**

We assume that the students are familiar with basic probabilistic concepts like random variables, expectation and higher moments, probability distributions, independence, and

the central limit theorem. Furthermore, we assume that the students have followed a basic course in calculus, including Riemann integration.

**Aim of the course**

The course is an introduction to a rigorous treatment of probability theory based on measure- and Lebesgue integration theory. We will develop the necessary measure- and integration theory together with the probabilistic interpretation, so that the two subjects (measure theory and probability) are developed simultaneously. Measure-theoretic topics include sigma-algebras, measures, Lebesgue integrals, convergence theorems, and the Radon-Nikodym theorem. Probabilistic topics include conditional probability and expectation, modes of convergence of random variables, characteristic functions, laws of large numbers and martingales.

**Rules about Homework/Exam**

There is one final exam, at the end of the course. In addition, there will be three small 45-minutes tests in the third hour of the lecture. These tests are not compulsory, and can only be used to improve your final grade. More precisely, a perfect score in the three small exams will increase your final grade by 1 point. In order to pass the course, you need to score at least a 5.0 for the final exam.

**Lecture notes/Literature**

The book Probability and Measure, by Patrick Billingsley, provided by us as a pdf.

**Lecturers**

Ronald Meester and Maximilian Engel

- Docent: Shreehari Bodas
- Docent: Aafko Boonstra
- Docent: Maximilian Engel
- Docent: Ronald Meester
- Docent: Yury Tavyrikov