  We prove that the upper envelope of a family of subharmonic functions defined
on an open subset of $\mathbb{R}^{N}$, $(N\geq2)$, that is finite every where,
is locally bounded above outside a closed nowhere dense set with no bounded
components. Then we conclude as a consequence that a separately subharmonic
function is subharmonic outside a closed nowhere dense set with no bounded
components. It generalizes a result due to Cegrell and Sadullaev.
