Family of Subharmonic Functions and Separately Subharmonic Functions

Abstract

We prove that the upper envelope of a family of subharmonic functions defined on an open subset of ${\mathbb{R}}^N$, $(N\ge 2)$, 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.

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References in corpus (1)

• Subharmonic functions, generalizations and separately subharmonic functions

Cited by in corpus (1)

• Continuity of Subharmonic Functions