“Packing measure and a theorem of Besicovitch”
Packing measures, as well as Hausdorff measures, are used to provide fine information on the size of fractal sets. For many random sets, especially related to Brownian motion, packing measures (rather than Hausdorff measures) provide the right concept to measure the size of the set.
Packing measures are in some sense dual to Hausdorff measures, and in many situations it is expected that results which are valid for one of them have their dual version for the other. In the talk I will discuss a theorem of Besicovitch for Hausdorff measures and I will show
that its version for packing measures does not hold in general.