Erschienen in:

2001 | OriginalPaper | Buchkapitel

Infima of Families of Superharmonic Functions

verfasst von : Joseph L. Doob

Erschienen in: Classical Potential Theory and Its Probabilistic Counterpart

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

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If Γ is a class of extended real-valued functions on a set D, a function v on D will be called a majorant [minorant] of Γ if v ≥ u [v ≤ u] for every u in Γ. If D is an open subset of ℝN, the least superharmonic majorant [greatest subharmonic minorant] of Γ, if such a function exists, will be denoted by LM_DΓ [GM_DΓ], or by LM_Du [GM_Du] if Γ = {u} is a singleton.

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