An extended Monge-Ampère operator

I will discuss a joint work in progress with Mats Andersson and David Witt Nyström. We introduce a class of plurisubharmonic functions $\mathcal G$, for which there is a natural Monge-Ampère operator with nice continuity properties. The class $\mathcal G$ includes plurisubharmonic functions with analytic singularities and has certain convexity properties, and thus it has a quite rich structure.