Infima of superharmonic functions |
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Authors: | Mohammad Alakhrass Wolfhard Hansen |
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Institution: | 1. Department of Mathematics and Statistics, McGill University, Burnside Hall, Room 805 Sherbrooke W., Montreal, QC, H3A?2K6, Canada 2. Fakult?t für Mathematik, Universit?t Bielefeld, Postfach 100 131, DE-33501, Bielefeld, Germany
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Abstract: | Let Ω be a Greenian domain in ℝ d , d≥2, or—more generally—let Ω be a connected -Brelot space satisfying axiom D, and let u be a numerical function on Ω, , which is locally bounded from below. A short proof yields the following result: The function u is the infimum of its superharmonic majorants if and only if each set {x:u(x)>t}, t∈ℝ, differs from an analytic set only by a polar set and , whenever V is a relatively compact open set in Ω and x∈V. |
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