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.
Received: 15 December 2000 / Published online: 1 February 2002