After successful completion of the course, students are able to explain important theorems and definitions from the topics listed below and to apply the methods of the field to solving selected problems.
Theory of measure and probability spaces, Lebesgue integral, Radon-Nikodym theorem, product spaces, conditional expectation, types of convergence, laws of large numbers, central limit theorem
Kusolitsch: Maß- und Wahrscheinlichkeitstheorie, Springer, Ash: Probability and Measure Theory, Academic Press Billingsley: Probability and Measure, Wiley Capinski-Kopp: Measure,Integral and Probability, Springer Elstrodt: Maß- Integrationstheorie, Springer Halmos: Measure Theory, Springer
