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- Carathéodory's_extension_theorem abstract "See also Carathéodory's theorem for other meanings.In measure theory, Carathéodory's extension theorem (named after the Greek mathematician Constantin Carathéodory) states that any measure defined on a given ring R of subsets of a given set Ω can be extended to the σ-algebra generated by R, and this extension is unique if the measure is σ-finite. Consequently, any measure on a space containing all intervals of real numbers can be extended to the Borel algebra of the set of real numbers. This is an extremely powerful result of measure theory, and proves, for example, the existence of the Lebesgue measure.".
- Carathéodory's_extension_theorem wikiPageID "4026968".
- Carathéodory's_extension_theorem wikiPageRevisionID "604777963".
- Carathéodory's_extension_theorem subject Category:Theorems_in_measure_theory.
- Carathéodory's_extension_theorem comment "See also Carathéodory's theorem for other meanings.In measure theory, Carathéodory's extension theorem (named after the Greek mathematician Constantin Carathéodory) states that any measure defined on a given ring R of subsets of a given set Ω can be extended to the σ-algebra generated by R, and this extension is unique if the measure is σ-finite. Consequently, any measure on a space containing all intervals of real numbers can be extended to the Borel algebra of the set of real numbers.".
- Carathéodory's_extension_theorem label "Carathéodory's extension theorem".
- Carathéodory's_extension_theorem label "Maßerweiterungssatz von Carathéodory".
- Carathéodory's_extension_theorem label "Théorème d'extension de Carathéodory".
- Carathéodory's_extension_theorem label "Теорема Каратеодори о продолжении меры".
- Carathéodory's_extension_theorem label "カラテオドリの拡張定理".
- Carathéodory's_extension_theorem sameAs Carath%C3%A9odory's_extension_theorem.
- Carathéodory's_extension_theorem sameAs Maßerweiterungssatz_von_Carathéodory.
- Carathéodory's_extension_theorem sameAs Théorème_d'extension_de_Carathéodory.
- Carathéodory's_extension_theorem sameAs カラテオドリの拡張定理.
- Carathéodory's_extension_theorem sameAs Q2631152.
- Carathéodory's_extension_theorem sameAs Q2631152.
- Carathéodory's_extension_theorem wasDerivedFrom Carathéodory's_extension_theorem?oldid=604777963.