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In this paper we study a p harmonic measure, associated with a positive pharmonic function \hat{u} defined in an open set O, subset of R^n, andvanishing on a portion \Gamma of boundary of O. If p>n we show that this pharmonic measure is concentrated on a set of \sigma- finite H^{n-1} measurewhile if p=n the same conclusion holds provided \Gamma is uniformly fat in thesense of n capacity.

Hausdorff dimension and $\sigma$ finiteness of $p-$harmonic measures in space when $p\geq n$