Syllabus
1. Basic of topology (product and relativ topology, Tikhonov theorem, random maps, random variables, probability measures on topological spaces, weak convergence of probability measures).
2. Metric spaces (Polish space, Prokhorov theorem, Banach space).
3. Topology of the space of functions (Borel sigma-algebra, Daniell-Kolmogorov theorem, cylindric sigma-algebra, random process).
4. Properties of spaces C[0,1] and D[0,1],
5. Donsker invariance princip and applications.
Annotation
Probability measures on metric spaces. Prokhoroff theorem.
Properties of C[0,1] and D[0,1]. Donsker invariance principle.