FrÉChet–Kolmogorov Theorem



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What is Fréchet–Kolmogorov theorem?

In functional analysis, the Fréchet–Kolmogorov theorem (the names of Riesz or Weil are sometimes added as well) gives a necessary and sufficient condition for a set of functions to be relatively compact in an Lp space. It can be thought of as an Lp version of the Arzelà–Ascoli theorem, from which it can be deduced. The theorem is named after Maurice René Fréchet and Andrey Kolmogorov.

Technology Types

compactness theoremmathematical theorempropositionstatementtheoremtheorems in functional analysistheory


Frechet-Kolmogorov theoremFréchet-Kolmogorov theoremFrechet–Kolmogorov theoremKolmogorov-Riesz theorem


Satz von Kolmogorow-Riesz (de)Théorème de Fréchet-Kolmogorov (fr)フレシェ=コルモゴロフの定理 (ja)

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