On the approximation of weakly plurifinely plurisubharmonic functions

In this note, we study the approximation of singular plurifinely plurisubharmonic function $u$ defined on a plurifinely domain $\mathrm{\Omega }$. Under some conditions, we prove that $u$ can be approximated by an increasing sequence of plurisubharmonic functions defined on Euclidean neighborhoods of $\mathrm{\Omega }$.