论文标题
plurisubharmonic功能的准超声酮收敛性
Quasi-monotone convergence of plurisubharmonic functions
论文作者
论文摘要
贝德福德·泰勒（Bedford-Taylor）在80年代将复杂的Monge-ampère操作员定义为局部有限的Plurisubharmonic功能。该定义已扩展到紧凑的复杂流形，并为各种无限的Quasi-plurisubharmonic功能。由于该操作员对于$ l^{1} $ - 拓扑并不连续，因此在过去的几十年中引入了一些更强的拓扑，以补救这一点，同时保持有效的紧凑标准。本说明的目的是表明，这些更强的拓扑基本上等同于我们在此介绍和研究的天然准单座拓扑。
The complex Monge-Ampère 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 unbounded quasi-plurisubharmonic functions by various authors. As this operator is not continuous for the $L^{1}$-topology, several stronger topologies have been introduced over the last decades to remedy this, while maintaining efficient compactness 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.
