A Marstrand type theorem for measures with cube density in general dimension

Andrew Lorent

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Submission date: 09. Jan. 2001 (revised version: March 2003)
Pages: 36
published in: Mathematical proceedings of the Cambridge Philosophical Society, 137 (2004) 3, p. 657-696 
MSC-Numbers: 28A75
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Abstract:

With a view to generalising rectifiability and density results to more general spaces we prove the following: Let denote Hausdorff s measure in . Let . Let be a subset of positive locally finite Hausdorff s-measure with the property

then s is an integer and S has a weak tangent at almost every point.