On dimension of porous measures

We introduce a notion of mean porosity for measures and obtain dimensional bounds for mean-porous and porous measures. As a corollary we generalize to all porous Borel measures the estimate obtained recently by J.-P. Eckmann, E. Järvenpää, and M. Järvenpää for porous measures satisfying the doubling condition. We also discuss various generalizations of this notion and possible applications