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.
Signed measures , Lebesgue spaces, Radon-Nikodym theorem, product spaces, conditional expectation, concepts of convergence, probability spaces, laws of large numbers, limit theorems,
Martingales
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
