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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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
|Deposited By:||Mr Pablo Shmerkin|
|Deposited On:||17 January 2011|