  Let $D$ be a bounded domain in $\mathbb C^n$. We study approximation of (not
necessarily bounded from above) $m-$subharmonic function $D$ by continuous
$m-$subharmonic ones defined on neighborhoods of $\overline{D}$. We also
consider the existence of a $m-$subharmonic function on $D$ whose boundary
values coincides with a given real valued continuous function on $\partial D$
except for a sufficiently small subset of $\partial D.$
