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In a recent article we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big pieces of Lipschitz graphs, and a sufficient condition for …

A Radon measure $\mu$ is $n$-rectifiable if it is absolutely continuous with respect to ${\mathcal{H}}^n$ and $\mu$-almost all of supp$\mu$ can be covered by Lipschitz images of ${\mathbb{R}}^n$. In this paper we give two sufficient conditions for …

A Radon measure $\mu$ is $n$-rectifiable if it is absolutely continuous with respect to $n$-dimensional Hausdorff measure and $\mu$-almost all of supp$\mu$ can be covered by Lipschitz images of ${\mathbb{R}}^n$⁠. In this paper, we give a necessary …

We give a new characterization of Sobolev-Slobodeckij spaces $W^{1+s,p}(\mathrm{\Omega })$ for $pn$ and $\frac{n}{p}