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We study dimensional properties of porous measures on R n . As a corollary of a theorem describing the local structure of nearly uniformly porous measures we prove that the packing dimension of any Radon measure on R n has an upper bound depending on porosity. This upper bound tends to n - 1 as porosity tends to its maximum value.

Porous measures on $\mathbb {R}^{n}$: Local structure and dimensional properties