Infima of superharmonic functions

Mohammad Alakhrass Department of Mathematics and Statistics, McGill University Wolfhard Hansen Fakultät für Mathematik, Universität Bielefeld

Functional Analysis Mathematical Physics mathscidoc: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$x$∈$V$.
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@inproceedings{mohammad2010infima,
  title={Infima of superharmonic functions},
  author={Mohammad Alakhrass, and Wolfhard Hansen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203633734182029},
  booktitle={Arkiv for Matematik},
  volume={50},
  number={2},
  pages={231-235},
  year={2010},
}
Mohammad Alakhrass, and Wolfhard Hansen. Infima of superharmonic functions. 2010. Vol. 50. In Arkiv for Matematik. pp.231-235. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203633734182029.
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