Let $\Omega$ be an open set in $\C^n,$ and let $A$ be a closed pluripolar set in $\Omega,$ is there a notion of dimension of $A$ in such a way that the following theorem is true ?

Theoem

Let $\phi$ be a plurisubharmonic function on $\Omega \setminus A$ (not necessarly assumed to be locally bounded above near $A$) and assume that the (real) codimension of $A$ is at least $3,$ then the function $\phi$ extends to a plurisubharmonic function on $\Omega.$

I think I can prove the theorem in case $A$ is complex analytic.