Subextension and approximation of $m$-subharmonic functions with given boundary values

In this paper we establish a result on subextension of $m$-subharmonic functions in the class ${\mathcal{F}}_m(\mathrm{\Omega },f)$ without changing the hessian measures. As application, we approximate a $m$-subharmonic function with given boudary value by an increasing sequence of $m$-subharmonic functions defined on larger domains.