Weakly solutions to the complex Monge-Amp\`ere equation on bounded plurifinely hyperconvex domains

Abstract

Let $\mu$ be a non-negative measure defined on bounded $\mathcal F$-hyperconvex domain $\Omega$. We are interested in giving sufficient conditions on $\mu$ such that we can find a plurifinely plurisubharmonic function satisfying $NP (dd^c u)^n =\mu$ in $QB(\Omega)$.