Zusammenfassung für den Vortrag am 11.10.2005 (11:15 Uhr)

Andrew Lorent (MPI MIS, Leipzig)

A Marstrand theorem for measures with polytope density

We provide a partial generalisation of the classic theorem of Marstrand that states, given a Radon measure in Euclidean space with positive finite s-density and almost all point s, s has to be an integer. Our theorem holds for all finite dimensional normed vector spaces whose unit ball is a polytope, over the restricted density range s in [0,2].