Removable sets for subharmonic functions

Juhani Riihentaus

Vol. 194 (2000), No. 1, 199–208

DOI: 10.2140/pjm.2000.194.199

Abstract

It is a classical result that a closed exceptional polar set is removable for subharmonic functions which are bounded above. Gardiner has shown that in the case of a compact exceptional set the above boundedness condition can be relaxed by imposing certain smoothness and Hausdorff measure conditions on the set. We give related results for a closed exceptional set, by replacing the smoothness and Hausdorff measure conditions with one sole condition on Minkowski upper content.

Milestones

Received: 9 September 1998

Revised: 26 January 1999

Published: 1 May 2000