  Using recent development in Poletsky theory of discs, we prove the following
result:
  Let $X,$ $Y$ be two complex manifolds, let $Z$ be a complex analytic space
which possesses the Hartogs extension property, let $A$ (resp. $B$) be a non
locally pluripolar subset of $X$ (resp. $Y$).
  We show that every separately holomorphic mapping
  $f: W:=(A\times Y) \cup (X\times B)\longrightarrow Z$ extends to a
holomorphic mapping $\hat{f}$ on $\hat{W}:=\left\lbrace(z,w)\in X\times Y:\
\widetilde{\omega}(z,A,X)+\widetilde{\omega}(w,B,Y)<1 \right\rbrace$ such that
$\hat{f}=f$ on $W\cap \hat{W},$ where $\widetilde{\omega}(\cdot,A,X)$ (resp.
$\widetilde{\omega}(\cdot,B,Y))$ is the plurisubharmonic measure of $A$ (resp.
$B$) relative to $X$ (resp. $Y$).
  Generalizations of this result for an $N$-fold cross are also given.
