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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 meanporosity. The upper bound tends to $d-1$ as mean porosity tends to its maximumvalue. 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 meanporous measures are not necessarily approximable by mean porous sets. We verifythis by constructing an example of a mean porous measure $\mu$ on $\mathbb R$such that $\mu(A)=0$ for all mean porous sets $A\subset\mathbb R$.



Author: D. Beliaev, E. Järvenpää, M. Järvenpää, A. Käenmäki, T. Rajala, S. Smirnov, V. Suomala

Source: https://arxiv.org/



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