下调和函数族与分离的下调和函数
Family of Subharmonic Functions and Separately Subharmonic Functions
摘要：
我们证明了一个家庭的下调和函数定义在一个开放的$\mathbb{R}^{N}$，$(N\geq2)$，这是有限的每一个地方，是局部有界的上以外的封闭疏集没有有界的组件。作为推论，我们得到一个单独的下调和函数在一个没有有界分量的闭疏集外是次调和函数。它推广了Cegrell和Sadullaev的一个结果。
英文摘要：
We prove that the upper envelope of a family of subharmonic functions defined on an open subset of $\mathbb{R}^{N}$, $(N\geq2)$, that is finite every where, is locally bounded above outside a closed nowhere dense set with no bounded components. Then we conclude as a consequence that a separately subharmonic function is subharmonic outside a closed nowhere dense set with no bounded components. It generalizes a result due to Cegrell and Sadullaev.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
