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.
Comment: v2: 23 pages, 6 figures. Updated references. Accepted to J. London Math. Soc