We study an ordering of measures induced by plurisubharmonic functions. This ordering arises naturally in connection with problems related to negative plurisubharmonic functions. We study maximality with respect to the ordering and a related notion of minimality for certain plurisubharmonic functions. The ordering is then applied to the problem of weak*-convergence of measures, in particular Monge Ampere measures.

For μ a positive measure, we estimate the pluricomplex potential of μ, Pμ(x)=∫Ωg(x,y)dμ(y), where g(x,y) is the pluricomplex Green function (relative to Ω) with pole at y.

Poletsky has introduced a notion of plurisubharmonicity for functions defined on compact sets in C^{n}. We show that these functions can be completely characterized in terms of monotone convergence of plurisubharmonic functions defined on neighborhoods of the compact.

In this note we consider radially symmetric plurisubharmonic functions and the complex Monge–Ampère operator. We prove among other things a complete characterization of unitary invariant measures for which there exists a solution of the complex Monge–Ampère equation in the set of radially symmetric plurisubharmonic functions. Furthermore, we prove in contrast to the general case that the complex Monge–Ampère operator is continuous on the set of radially symmetric plurisubharmonic functions. Finally we characterize radially symmetric plurisubharmonic functions among the subharmonic ones using merely the laplacian.