The contents of this course are basic for all advanced courses in probability and statistics. Interested students should to have a basic knowledge in stochastics comparable to that provided by an introductory university course (8-9 ECTS) in that field.
From the contents: Measure theoretic foundations (systems of sets, measures, measure extension theorem, integral with respect to a measure, monotone convergence, dominated convergence, the Radon-Nikodym theorem, Fubini's theorem) and probability theory (Kolmogorov's axioms, random variables, indepencence, Zero-one-law, charakteristic functions, notions of convergence, Law of large numbers, Central limit theorem, multivariate normal distribution, conditional expectation and conditional distributions, martingales).
