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In mathematics, the bipolar theorem is a theorem in functional analysis that characterizes the bipolar (that is, the polar of the polar) of a set. In convex analysis, the bipolar theorem refers to a necessary and sufficient conditions for a cone to be equal to its bipolar. The bipolar theorem can be seen as a special case of the Fenchel–Moreau theorem.

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  • In mathematics, the bipolar theorem is a theorem in functional analysis that characterizes the bipolar (that is, the polar of the polar) of a set. In convex analysis, the bipolar theorem refers to a necessary and sufficient conditions for a cone to be equal to its bipolar. The bipolar theorem can be seen as a special case of the Fenchel–Moreau theorem. (en)
  • En mathématiques, le théorème bipolaire est un théorème d'analyse convexe qui fournit les conditions nécessaires et suffisantes pour qu'un cône soit égal à son cône bipolaire. Le théorème bipolaire peut être vu comme un cas particulier du théorème de Fenchel-Moreau. (fr)
  • 数学において、双極定理(そうきょくていり、英: bipolar theorem)とは、錐がその双極と等しいための必要十分条件を与える凸解析の一定理である。双極定理は、フェンシェル=モローの定理の特別な場合と見なすことが出来る。 (ja)
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  • In mathematics, the bipolar theorem is a theorem in functional analysis that characterizes the bipolar (that is, the polar of the polar) of a set. In convex analysis, the bipolar theorem refers to a necessary and sufficient conditions for a cone to be equal to its bipolar. The bipolar theorem can be seen as a special case of the Fenchel–Moreau theorem. (en)
  • En mathématiques, le théorème bipolaire est un théorème d'analyse convexe qui fournit les conditions nécessaires et suffisantes pour qu'un cône soit égal à son cône bipolaire. Le théorème bipolaire peut être vu comme un cas particulier du théorème de Fenchel-Moreau. (fr)
  • 数学において、双極定理(そうきょくていり、英: bipolar theorem)とは、錐がその双極と等しいための必要十分条件を与える凸解析の一定理である。双極定理は、フェンシェル=モローの定理の特別な場合と見なすことが出来る。 (ja)
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  • Bipolarensatz (de)
  • Bipolar theorem (en)
  • Théorème bipolaire (fr)
  • 双極定理 (ja)
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