Quasi-monotone convergence of plurisubharmonic functions

The complex Monge-Ampere operator has been defined for locally bounded plurisubharmonic functions by Bedford-Taylor in the 80's. This definition has been extended to compact complex manifolds, and to various classes of mildly un-bounded quasi-plurisubharmonic functions by various authors. As this operator is not continuous for the L1-topology, several stronger topologies have been introduced over the last decades to remedy this, while maintaining efficient compact-ness criteria. The purpose of this note is to show that these stronger topologies are essentially equivalent to the natural quasi-monotone topology that we introduce and study here.(c) 2023 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).