Dimension, entropy, and the local distribution of measures

Published 27 Oct 2011 in math.CA and math.DS | (1110.6011v2)

Abstract: 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.

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