After finishing the course, the student should
- know what a measure is;
- be aware of the problem of measurability of sets and be able to indicate its solution;
- be able to discuss integrability of a function with respect to a measure;
- know that probability theory is based on measure theory;
- be able to identify notions from probability theory with notions from measure theory an integration theory;
- understand basic concepts of convergence and be able to apply convergence theorems.
The course is an introduction into measure and integration theory, with special attention to the fundamental role of this theory in probability. Contents: measure, Lebesgue measure, measure space, probability space, measurable function, stochastic variable, integral, Lebesgue integral, integrable function, expectation, product measure, Radon-Nikodym theorem, limit theorems.