Weak convergence of currents

We give certain conditions to guarantee weak convergence ukTk → uT, where uk, u are plurisubharmonic functions and Tk, T are positive closed currents. As applications we obtain that convergence in capacity of plurisubharmonic functions uk implies weak convergence of the complex Monge-Ampère measures (ddcuk)n if all of the plurisubharmonic functions uk are bounded below by one of some sorts of plurisubharmonic functions.