Mathematics – Classical Analysis and ODEs
Scientific paper
2007-05-16
Mathematics
Classical Analysis and ODEs
Revised version
Scientific paper
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 $A\subset\mathbb R$.
Beliaev Dmitry
Järvenpää Esa
Järvenpää Maarit
Kaenmaki Antti
Rajala Tapio
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