Local property of maximal plurifinely plurisubharmonic functions
  In this paper, we prove that a continuous $\mathcal F$-plurisubharmonic functions defined in an $\mathcal F$-open set in $\mathbb C^n$ is $\mathcal F$-maximal if and only if it is $\mathcal F$-locally $\mathcal F$-maximal. 
Nguyen Xuan Hong and Hoang Viet
math.CV