A generalization of Marstrand's theorem

2014/12/13 by López, Jorge Erick, Moreira, Carlos Gustavo, Silva, Waliston Luiz
#28A75 #28A78 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1412.4242

Abstract

In this paper we prove two general results related to Marstrand's projection theorem in a quite general formulation over separable metric spaces under a suitable transversality hypothesis (the "projections" are in principle only measurable) - the result is flexible enough to, in particular, recover most of the classical Marstrand-like theorems. Our proofs use simpler tools than many classical works in the subject, where some techniques from harmonic analysis or special geometrical structures on the spaces are used.

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