A note on Sobolev-Lorentz Capacity and Hausdorff measure

Abstract

In this paper we give an elementary proof that sets of zero p,1-Sobolev-Lorentz capacity are Hn-p-null sets independently of non-linear potential theory. We further show that there exists a set of Sobolev-Lorentz-(p,1) capacity equal zero with Hausdorff dimension equal n-p.

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