Foundations of Probability Theory

This course aims at introducing from an advanced point of view the fundamental concepts of probability theory. Moreover, various forms of convergence are introduced and studied and some important limit results and tools (such as the Fourier transform/characteristic function) are illustrated. At the beginning of the course some elements of measure theory and integration theory (the Lebesgue integral) are given. Some proofs are sketched or omitted in order to have more time for examples, applications and exercises.