Weak convergence of currents (Q943383)

The author gives various conditions to ensure the weak convergence \(u_kT_k\rightarrow uT\) of currents , where \(u_k, u\) are plurisubharmonic functions and \(T_k, T\) are positive closed currents. As an application, the author proves that if the \(u_k\)'s are bounded below by some plurisubharmonic function with bounded boundary values, then convergence \(u_k\rightarrow u\) in capacity implies weak convergence of the complex Monge-Ampère measures \((dd^cu_k)^n\rightarrow (dd^cu)^n\).