Abstract
This paper examines the boundary behaviour of superharmonic functions on a half-space in terms of their behaviour along lines normal to the boundary. It is shown that, if the set of lines along which such functions grow quickly is (in a certain sense) metrically dense, then the set of lines along which they are bounded below is topologically small.
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Gardiner, S.J. Boundary growth theorems for superharmonic functions. Ark. Mat. 37, 255–273 (1999). https://doi.org/10.1007/BF02412214
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DOI: https://doi.org/10.1007/BF02412214