  In this paper we study approximations of functions of Sobolev spaces
$W^2_{p,\loc}(\Omega)$, $\Omega\subset\mathbb R^n$, by Lipschitz continuous
functions. We prove that if $f\in W^2_{p,\loc}(\Omega)$, $1\leq p<\infty$, then
there exists a sequence of closed sets $\{A_k\}_{k=1}^{\infty},A_k\subset
A_{k+1}\subset \Omega$, such that the restrictions $f \vert_{A_k}$ are
Lipschitz continuous functions and $\cp_p\left(S\right)=0$,
$S=\Omega\setminus\bigcup_{k=1}^{\infty}A_k$. Using these approximations we
prove the change of variables formula in the Lebesgue integral for mappings of
Sobolev spaces $W^2_{p,\loc}(\Omega;\mathbb R^n)$ with the Luzin
capacity-measure $N$-property.
