After successful completion of the course, students are able to work with set systems, measures, and abstract integrals and analyze general probability measures and special distributions and random variables or measurable functions
Probabilty Spaces, distributions, measure theoretic foundations of probability theory, independence and conditional probability, distribution functions, random variables, Lebesgue integral and expectation, comparison of Riemann and Lebesgue integral, laws of large numbers
I will use mostly:
A. Klenke, Wahrscheinlichkeitstheorie (available in electronic form at the TU WIen library)
and Chapter 1 of
Shiryaev, Probability Volume 1 for the concepts in elementary probability theory
Other literature:
N. Kusolitsch, Mass- und Wahrscheinlichkeitstheorie (available in electronic form at the TU WIen library)
Williams, D.: Probability with Martingales, Cambridge University Press, Cambridge, 2010.
