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

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