ACL and differentiability of a generalization of quasi-conformal maps

It is established that $Q$-homeomorphisms (in the sense of O. Martio) defined in $\mathbb{R}^n$, $n\geqslant2$, are absolutely continuous on lines. Furthermore, they belong to the Sobolev class $W_{\mathrm{loc}}^{1,1}$ and are differentiable almost everywhere for $Q\in L^{1}_{\mathrm{loc}}$.