Murat Akman, John Lewis, Andrew Vogel
Abstract: In this paper we study a $p$ harmonic measure, associated with a positive $p$ harmonic function $\hat{u}$ defined in an open set $O\subset \mathbb R^n$, and vanishing on a portion $\Gamma$ of $\partial O$. 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.
ArXiv: 1306.5617