Self-similar sets and measures

A major theme in the theory of fractals is that of self—similarity: the whole fractal set is composed of smaller parts which are geometrically similar to whole set. There are several ways to formulate this concept in a mathematically rigorous way. Неге I will deal with Hutchinson’s definition of self-similarity. It is the purpose of this lecture to collect some of the basic results concerning the Hausdorff dimension, Hausdorff measure and local structure of self-similar sets and measures. I am not striving for completeness but rather use my own research interests as a guide to the results and problems in the area. Most of the proofs are omitted. Interested roaders are refered to the literature.