Maattheorie en Kansrekening

The goal of the course is to introduce students to measure and integration theory and learn how this is used in probability theory. The offered topics are: (1) sigma algebras and measures (2) Construction of measures, (3) Properties of the Lebesgue measure, (4) Lebesgue integration, (5) Monotone convergence theorem, Fatou's lemma, Dominated convergence theorem, (6) L^p-spaces, (7) Product measures and Fubini's theorem, (8) Independence (9) Borel Cantelli lemmas and applications, (10) Kolmogorov's zero-one law and applications, (11) Conditional expectation, and applications (12) convergence of random variables (almost sure, in probability, distributional), connection to Law of large numbers and Central Limit Theorem