Subextension of plurisubharmonic functions without changing the Monge–Ampère measures and applications
Volume 112 / 2014
Annales Polonici Mathematici 112 (2014), 55-66
MSC: 32U05, 32U15, 32W20.
DOI: 10.4064/ap112-1-5
Abstract
The aim of the paper is to investigate subextensions with boundary values of certain plurisubharmonic functions without changing the Monge–Ampère measures. From the results obtained, we deduce that if a given sequence is convergent in $C_{n-1}$-capacity then the sequence of the Monge–Ampère measures of subextensions is weakly$^*$-convergent. As an application, we investigate the Dirichlet problem for a nonnegative measure $\mu $ in the class $\mathcal {F}(\varOmega ,g)$ without the assumption that $\mu $ vanishes on all pluripolar sets.
