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

UDC 517.5 We establish a result on subextension of $m$-subharmonic functions in the class $\mathcal{F}_m(\Omega,f)$ without changing the Hessian measures. As application, we approximate an $m$-subharmonic function with given boundary value by an increasing sequence of $m$-subharmonic functions defined in larger domains.