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2011.7: The dimension of weakly mean porous measures: a probabilistic approach

2011.7: Pablo Shmerkin (2011) The dimension of weakly mean porous measures: a probabilistic approach.

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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 2000 > 28 Measure and integration
MSC 2000 > 37 Dynamical systems and ergodic theory
MIMS number:2011.7
Deposited By:Mr Pablo Shmerkin
Deposited On:17 January 2011

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