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 $n-1$ as porosity tends to its maximum value.