Syllabus
1. k-dimensional Hausdorff measure, Hausdorff dimension, covering theorems, Lebesgue density theorem. 2. Invariant measures on a compact topological group, Haar measure, integral-geometric measure. 3.
Disintegration theorem for measures on Cartesian products, existence of regular versions of conditional probabilities, random measure.
Annotation
Selected results completing the lecture NMMA203 Measure and Integration Theory, with respect to applications in probability theory> Hausdorff measure and dimension, Lebesgue density theorem, Haar measure, disintegration theorem.