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, martingales, and Brownian motion.
Rules about homework/exam
There is one final exam, at the end of the course. In addition, there will be two 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. Example: if you score a 5.8 for the final exam and your average grade for the two tests is 8.0, then your final grade is 5.8 + 0.8 = 6.6, which will be rounded to 6.5. The same rule applies to the resit; the 45-minutes tests remain valid.
Lecture notes/Literature
The book Probability and Measure, by Patrick Billingsley, provided by us as a pdf.
- Docent: Maximilian Engel
- Docent: Ronald Meester