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.
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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.
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