*Note that this course is cross-listed with the ELTE University and is held on their campus. Its schedule is set by ELTE. Time and location will be available by the beginning of September*

*Instructor:* Dr. Márton ELEKES
*Textbooks:* none

*Suggested reading:*

K. Falconer: Fractals. A very short introduction. Oxford University Press, 2013.

P. Mattila: Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability. Cambridge University Press, 1995.

P. R. Halmos: Measure Theory. D. Van Nostrand, 1950.

J. C. Oxtoby: Measure and category. A survey of the analogies between topological and measure spaces. Springer, 1980.

W. Rudin: Functional analysis. McGraw-Hill, 1973.

*Prerequisits:*
introductory courses to measure theory, group theory and topology
*Course description:*

Fractal geometry: self-similar sets, Hausdorff measures, Hausdorff dimension,
box dimension.

Haar measure: existence, uniqueness, modular function, Pontryagin duality and the structure of locally compact groups.

Lipschitz functions: Theorems of Kirszbraun and Rademacher, the cases of Euclidean, Hilbert and Banach spaces.

Genericity and prevalence: Baire category, Christensen's notion of Haar null sets in non-locally compact groups, constructions of exotic objects.