The dimension of weakly mean porous measures: a probabilistic approach
Classical Analysis and ODEs
2013-03-25 v1 Dynamical Systems
Probability
Abstract
Using probabilistic ideas, we prove that the packing dimension of a mean porous measure is strictly smaller than the dimension of the ambient space. Moreover, we give an explicit bound for the packing dimension, which is asymptotically sharp in the case of small porosity. This result was stated in [D. B. Beliaev and S. K. Smirnov, "On dimension of porous measures", Math. Ann. 323 (2002) 123-141], but the proof given there is not correct. We also give estimates on the dimension of weakly mean porous measures, which improve another result of Beliaev and Smirnov.
Cite
@article{arxiv.1010.1394,
title = {The dimension of weakly mean porous measures: a probabilistic approach},
author = {Pablo Shmerkin},
journal= {arXiv preprint arXiv:1010.1394},
year = {2013}
}
Comments
21 pages, 2 figures