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Convergence in Capacity

Yang Xing — 2008

Annales de l’institut Fourier

We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity C n of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity C n - 1 of functions in some case. As applications we give certain stability theorems...

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