  Let $\Omega,\Omega'\subset\mathbb{R}^3$ be Lipschitz domains, let
$f_m:\Omega\to\Omega'$ be a sequence of homeomorphisms with prescribed
Dirichlet boundary condition and $\sup_m
\int_{\Omega}(|Df_m|^2+1/J^2_{f_m})<\infty$. Let $f$ be a weak limit of $f_m$
in $W^{1,2}$. We show that $f$ is invertible a.e., more precisely it satisfies
the (INV) condition of Conti and De Lellis and thus it has all the nice
properties of mappings in this class.
  Generalization to higher dimensions and an example showing sharpness of the
condition $1/J^2_f\in L^1$ are also given. Using this example we also show that
unlike the planar case the class of weak limits and the class of strong limits
of $W^{1,2}$ Sobolev homeomorphisms in $\mathbb{R}^3$ are not the same.
