Shmerkin, Pablo (2011) The dimension of weakly mean porous measures: a probabilistic approach. [MIMS Preprint]
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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.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | Porosity, packing dimension, entropy averages, CICADA |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 28 Measure and integration MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory |
| Depositing User: | Mr Pablo Shmerkin |
| Date Deposited: | 17 Jan 2011 |
| Last Modified: | 20 Oct 2017 14:12 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1566 |
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