Mappings of finite distortion: Hausdorff measure of zero sets

Abstract.

We prove that a for a mapping f of finite distortion $K\in L^{p/(n-p)}$, the $(n-p)$-Hausdorff measure of any point preimage is zero provided $J_f$ is integrable, $Df\in L^s$ with $s>p$, and the multiplicity function of f is essentially bounded. As a consequence for $p=n-1$ we obtain that the mapping is then open and discrete.