Rad\'{o}- type theorem for subharmonic and plurisubharmonic functions

Sławomir Dinew; Żywomir Dinew

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arXiv · 2109.10842

Rad\'{o}- type theorem for subharmonic and plurisubharmonic functions

Sławomir Dinew·Żywomir Dinew

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Abstract

We observe that a recent result by Gardiner and Sj\"odin, solving a problem of Kr\'{a}l on subharmonic functions, can be easily generalized to yield a somewhat stronger result. This can be combined with a viscosity technique of ours, which we slightly improve, to obtain Rad\'{o}- type theorems for plurisubharmonic functions. Finally, we study the Borel complexity of the critical set and the set where the gradient does not exist finitely of subharmonic functions and general real valued functions.

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Sławomir Dinew, Żywomir Dinew. 2021-09-22. Rad\'{o}- type theorem for subharmonic and plurisubharmonic functions. https://arxiv.org/abs/2109.10842

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