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