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

We study the Monge-Amp\`ere operator $u \mapsto (\text{dd}^c u)^n$ and compare it with Dinh-Sibony's intersection product 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 $(\text{dd}^c u)^n$.