Prerequisites
The 'standard' basic probability and analysis courses taught in the mathematics BSc are prerequisites for this course. Measure theory and Lebesgue integration theory is built up 'from scratch' in the first part of this course. However, the course is probably rather difficult for those students who have not done any measure- and integration theory previously. In that case it may help to consult Rene Schilling's Measures, Integrals and Martingales, or Jeffrey Rosenthal's A First Look at Rigorous Probability Theory for some extra material on this topic.

Aim of the course
The course is meant to be an introduction to a rigorous treatment of probability theory based on measure- and Lebesgue integration theory. The first part of the course is an introduction to measure theory, including the following topics: sigma-algebra's, measures, measurable functions, the Lebesgue integral, convergence theorems, Lp-spaces, product measure, Fubini's theorem, absolute continuity and the Radon-Nikodym theorem. The second part is probabilistic, and includes

• Conditional probability and expectation
• Modes of convergence of random variables
• Characteristic functions
• Laws of large numbers
• Brownian motion

Lecturers

1. Dalia Terhesiu teaches the first part (measure theory)
2. Ronald Meester teaches the second part (probability theory)