To get acquainted with the basic terms and concepts of measure- and probability theory and to be able to apply this knowledge in problem solving

Probabilty Spaces, distributions, measure theoretic foundations of probability theory, independence and conditional probability, distribution functions,random variables, Lebesgue-Stieltjes-integral and expectation, comparison of Riemann and Lebesgue-integral

written and oral exam

illingsley, P.: Probability and Measure, Wiley, New York, 1986.

Elstrodt, J.:  Mass- und Integrationstheorie, Springer, Berlin, 2005.

Feller, W.:  An Introduction to Probability Theory and its Applications, Vol.1 and 2 Wiley, New York, 1968.

Georgii, H.O.,: Stochastik, de Gruyter, Berlin, 2002

Kusolitsch, N., : Mass- und Wahrscheinlichkeitstheorie, Springer, Wien, 2014

Rosanov, J.A.,: Stochastische Prozesse,Akademie, Berlin,1975

Williams, D.: Probability with Martingales, Cambridge University Press, Cambridge, 2010.