- Department of Forest Economics, Swedish University of Agricultural Sciences
We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampere measures. We find one type of convergence of complex Monge-Ampbre measures which is essentially equivalent to convergence in the capacity C-n of functions. We also prove that weak convergence of complex Monge-Ampere measures is equivalent to convergence in the capacity Cn-1 of functions in some case. As applications we give certain stability theorems of solutions of Monge-Ampere equations.
the complex Monge-Ampere operator; plurisubharmonic function; capacity
Annales de l'Institut Fourier
2008, Volume: 58, number: 5, pages: 1839-1861
Publisher: ANNALES INST FOURIER