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-Ampère measure $({\text{dd}}^{c}u{)}^n$.

Improved results. Revised presentation following referee's remarks. To appear in Indiana University Mathematics Journal