| dbo:abstract |
In mathematics, Helly's selection theorem (also called the Helly selection principle) states that a uniformly bounded sequence of monotone real functions admits a convergent subsequence.In other words, it is a sequential compactness theorem for the space of uniformly bounded monotone functions.It is named for the Austrian mathematician Eduard Helly.A more general version of the theorem asserts compactness of the space BVloc of functions locally of bounded total variation that are uniformly bounded at a point. The theorem has applications throughout mathematical analysis. In probability theory, the result implies compactness of a tight family of measures. (en) Le théorème de sélection de Helly a été établi par le mathématicien Eduard Helly en 1912. Ce théorème garantit qu'une suite de fonctions qui a des admet une sous-suite convergente. Il permet en particulier le passage à la limite sous le signe de l'intégrale de Stieltjes. (fr) 数学におけるヘリーの選択定理（ヘリーのせんたくていり、英: Helly's selection theorem）は、局所的に有界変動函数であり、ある点において一様有界であるような函数は収束部分列を持つ、ということを述べた定理である。言い換えると、空間 BVloc に対するコンパクト性定理である。オーストラリアの数学者であるエードゥアルト・ヘリーの名にちなむ。 この定理は解析学において広く応用されている。確率論において、この結果は緊密な測度の族のコンパクト性を意味する。 (ja) In matematica, con teorema di Helly ci si riferisce a più teoremi dovuti a Eduard Helly. Due di essi riguardano l'analisi funzionale e il passaggio al limite sotto il segno di integrale di Stieltjes. Questi due risultati affermano insieme che una successione di funzioni che sia, localmente, a variazione totale limitata e in un punto, ammette una sottosuccessione convergente. In altre parole, si ha un teorema di compattezza per lo spazio delle funzioni a variazione limitata . (it) |
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Le théorème de sélection de Helly a été établi par le mathématicien Eduard Helly en 1912. Ce théorème garantit qu'une suite de fonctions qui a des admet une sous-suite convergente. Il permet en particulier le passage à la limite sous le signe de l'intégrale de Stieltjes. (fr) 数学におけるヘリーの選択定理（ヘリーのせんたくていり、英: Helly's selection theorem）は、局所的に有界変動函数であり、ある点において一様有界であるような函数は収束部分列を持つ、ということを述べた定理である。言い換えると、空間 BVloc に対するコンパクト性定理である。オーストラリアの数学者であるエードゥアルト・ヘリーの名にちなむ。 この定理は解析学において広く応用されている。確率論において、この結果は緊密な測度の族のコンパクト性を意味する。 (ja) In matematica, con teorema di Helly ci si riferisce a più teoremi dovuti a Eduard Helly. Due di essi riguardano l'analisi funzionale e il passaggio al limite sotto il segno di integrale di Stieltjes. Questi due risultati affermano insieme che una successione di funzioni che sia, localmente, a variazione totale limitata e in un punto, ammette una sottosuccessione convergente. In altre parole, si ha un teorema di compattezza per lo spazio delle funzioni a variazione limitata . (it) In mathematics, Helly's selection theorem (also called the Helly selection principle) states that a uniformly bounded sequence of monotone real functions admits a convergent subsequence.In other words, it is a sequential compactness theorem for the space of uniformly bounded monotone functions.It is named for the Austrian mathematician Eduard Helly.A more general version of the theorem asserts compactness of the space BVloc of functions locally of bounded total variation that are uniformly bounded at a point. (en) |
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Théorème de sélection de Helly (fr) Teorema di Helly (it) Helly's selection theorem (en) ヘリーの選択定理 (ja) |
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