Weakly solutions to the complex Monge-Ampère 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 $NP(d{d}^{c}u{)}^n=\mu$ in $QB(\Omega )$.