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Packing dimension of mean porous measures

Beliaev, Dmitry
Järvenpää, E.
Järvenpää, M.
Käenmäki, A.
Rajala, T.
Suomala, V.
Published in Journal of the London Mathematical Society. 2009, vol. 80, no. 2, p. 514-530
Abstract We prove that the packing dimension of any mean porous Radon measure on $mathbb R^d$ may be estimated from above by a function which depends on mean porosity. The upper bound tends to $d-1$ as mean porosity tends to its maximum value. This result was stated in cite{BS}, and in a weaker form in cite{JJ1}, but the proofs are not correct. Quite surprisingly, it turns out that mean porous measures are not necessarily approximable by mean porous sets. We verify this by constructing an example of a mean porous measure $mu$ on $mathbb R$ such that $mu(A)=0$ for all mean porous sets $Asubsetmathbb R$.
arXiv: 0705.2447
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BELIAEV, Dmitry et al. Packing dimension of mean porous measures. In: Journal of the London Mathematical Society, 2009, vol. 80, n° 2, p. 514-530. https://archive-ouverte.unige.ch/unige:8527

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Deposited on : 2010-07-02

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