Subextension of plurisubharmonic functions without changing the Monge-Ampère measures and applications (Q2875408)

The authors generalise the results of \textit{U. Cegrell} and \textit{A. Zeriahi} [C. R., Math., Acad. Sci. Paris 336, No. 4, 305--308 (2003; Zbl 1025.31005)] and \textit{R. Czyż} and \textit{L. Hed} [Ann. Pol. Math. 94, No. 3, 275--281 (2008; Zbl 1161.32019)] by showing that subextension with boundary values of certain plurisubharmonic functions is always possible without changing the Monge-Ampère measures. As an application, they investigate the Dirichlet problem for a non-negative measure \(\mu \) in the Cegrell class \({\mathcal F}(\Omega , g)\) without the assumption that \(\mu \) vanishes on all pluripolar sets.