The dimension of weakly mean porous measures: a probabilistic approach

Details The dimension of weakly mean porous measures: a probabilistic approach The dimension of weakly mean porous measures: a probabilistic approach

2010-10-07

arxiv.org/abs/1010.1394v1

Mathematics

Classical Analysis and ODEs

21 pages, 2 figures

Scientific paper

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.

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