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Porous measures on $\mathbb {R}^{n}$: Local structure and dimensional properties
We study dimensional properties of porous measures on $\mathbb {R}^{n}$. 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 $\mathbb {R}^{n}$ has an upper bound depending on porosity. This upper bound tends to …