Calculus of Variations and Geometric Measure Theory
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A. Lorent

A Marstrand theorem for measures with polytope density

created by lorent on 31 Jan 2005
modified on 01 Feb 2009


Published Paper

Inserted: 31 jan 2005
Last Updated: 1 feb 2009

Journal: Math. Ann.
Volume: 338
Number: 2
Pages: 451-474
Year: 2007


We provide a partial generalisation of Marstrand theorem that 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 $[0,2]$.

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