Helly'S Selection Theorem

(Theory)

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What is Helly's selection theorem?

In mathematics, Helly's selection theorem states that a sequence of functions that is locally of bounded total variation and uniformly bounded at a point has a convergent subsequence. In other words, it is a compactness theorem for the space BVloc. It is named for the Austrian mathematician Eduard Helly. The theorem has applications throughout mathematical analysis. In probability theory, the result implies compactness of a tight family of measures.

Technology Types

compactness theorempropositionstatementtheoremtheorems in analysistheory

Synonyms

Helly selection theorem

Translations

Teorema di Helly (it)Théorème de sélection de Helly (fr)ヘリーの選択定理 (ja)

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