Márton Elekes:
Introduction to measure theory, geometric measure theory, geometric decompositions and descriptive set theory
The goal of this course is to introduce some basic notions, and discuss their basic properties that are needed in the later, more advanced courses of the Summer School. The topics covered are measure theory, geometric measure theory, Hausdorff measures, Hausdorff dimension, box dimension, groups of isometries, geometric decompositions, Borel sets and Baire category.