Intersection of (1,1)-currents and the domain of definition of the Monge-Ampere operator

Abstract: We study the Monge-Amp` ere operator within the framework of Dinh-Sibony's intersection theory defined via density currents. We show that if $u$ is a plurisubharmonic function belonging to the Blocki-Cegrell class, then the Dinh-Sibony $n$-fold self-product of $\text{dd}^c u$ exists and coincides with the classically defined Monge-Amp`ere measure $(\text{dd}^c u)^n$.