Dimension, entropy, and the local distribution of measures
  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. 
Tuomas Sahlsten, Pablo Shmerkin, Ville Suomala
math.CA math.DS