On a Monge-Ampère operator for plurisubharmonic functions with analytic singularities

Abstract: We study continuity properties of generalized Monge-Amp`ere operators for plurisubharmonic functions with analytic singularities. In particular, we prove continuity for a natural class of decreasing approximating sequences. We also prove a formula for the total mass of the Monge-Amp`ere measure of such a function on a compact K\"ahler manifold.