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arXiv:1110.6011 [math.CA]AbstractReferencesReviewsResources

Dimension, entropy, and the local distribution of measures

Tuomas Sahlsten, Pablo Shmerkin, Ville Suomala

Published 2011-10-27, updated 2012-09-26Version 2

We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local homogeneity, porosity and conical densities of measures.

Comments: v2: 23 pages, 6 figures. Updated references. Accepted to J. London Math. Soc
Categories: math.CA, math.DS
Subjects: 28A80, 28D20
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