# MathSciDoc: An Archive for Mathematician ∫

#### Functional AnalysisMathematical Physicsmathscidoc:1701.12021

Arkiv for Matematik, 50, (2), 231-235, 2010.6
Let Ω be a Greenian domain in ℝ^{$d$},$d$≥2, or—more generally—let Ω be a connected $\mathcal{P}$ -Brelot space satisfying axiom D, and let$u$be a numerical function on Ω, $u\not\equiv\infty$ , 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 $\int u\,d\mu_{x}^{V}\le u(x)$ , whenever$V$is a relatively compact open set in Ω and$x$∈$V$.
@inproceedings{mohammad2010infima,
title={Infima of superharmonic functions},