The Lusin-Privalov theorem for subharmonic functions

Gardiner, Stephen

doi:10.1090/S0002-9939-96-03879-8

The Lusin-Privalov theorem for subharmonic functions
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by Stephen J. Gardiner PDF

Proc. Amer. Math. Soc. 124 (1996), 3721-3727 Request permission

Abstract:

This paper establishes a generalization of the Lusin-Privalov radial uniqueness theorem which applies to subharmonic functions in all dimensions. In particular, it answers a question of Rippon by showing that no subharmonic function on the upper half-space can have normal limit $-\infty$ at every boundary point.

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