ABSTRACT
We prove that the upper envelope of a family of subharmonic functions defined on an open subset of ,
, 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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Acknowledgments
The author wishes to express his gratitude to Professor Ahmed Zeriahi who introduced the author to the fascinating world of potential theory, quiet some times ago. It is a pleasure to thank Professor Azimbay Sadullaev for his help and advice during the past years to present. This is also a pleasure to thank Professor Juhani Riihentaus for his generous help to the author during the last long years.
Disclosure statement
No potential conflict of interest was reported by the author.