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- Carathxc3xa9odorys_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.".
- Carathxc3xa9odorys_extension_theorem wikiPageExternalLink WEBcaratheodory.pdf.
- Carathxc3xa9odorys_extension_theorem wikiPageID "4026968".
- Carathxc3xa9odorys_extension_theorem wikiPageLength "7875".
- Carathxc3xa9odorys_extension_theorem wikiPageOutDegree "33".
- Carathxc3xa9odorys_extension_theorem wikiPageRevisionID "625355493".
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Borel_algebra.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Borel_set.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Carathxc3xa9odorys_theorem.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Category:Theorems_in_measure_theory.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Complement_(set_theory).
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Constantin_Carathéodory.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Content_(measure_theory).
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Countable.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Countable_set.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Disjoint_union.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Field_of_sets.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Fubinis_theorem.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Greeks.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Hahn-Kolmogorov_theorem.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Hahn–Kolmogorov_theorem.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Interval_(mathematics).
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Lebesgue_measure.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Lebesgue–Stieltjes_integration.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Loeb_measure.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Loeb_space.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Mathematician.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Measure_(mathematics).
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Measure_theory.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Outer_measure.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Power_set.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Pre-measure.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Real_number.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Ring_of_sets.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Semi-ring_of_sets.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Semiring.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Sigma-algebra.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Sigma-finite.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Stieltjes_measures.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Uncountable.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Uncountable_set.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Σ-algebra.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Σ-finite.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLink Σ-finite_measure.
- Carathxc3xa9odorys_extension_theorem wikiPageWikiLinkText "Carathéodory's extension theorem".
- Carathxc3xa9odorys_extension_theorem hasPhotoCollection Carathxc3xa9odorys_extension_theorem.
- Carathxc3xa9odorys_extension_theorem wikiPageUsesTemplate Template:!.
- Carathxc3xa9odorys_extension_theorem wikiPageUsesTemplate Template:=.
- Carathxc3xa9odorys_extension_theorem wikiPageUsesTemplate Template:Cite_book.
- Carathxc3xa9odorys_extension_theorem subject Category:Theorems_in_measure_theory.
- Carathxc3xa9odorys_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.".
- Carathxc3xa9odorys_extension_theorem label "Carathéodory's extension theorem".
- Carathxc3xa9odorys_extension_theorem sameAs Maßerweiterungssatz_von_Carathéodory.
- Carathxc3xa9odorys_extension_theorem sameAs Thxc3xa9orxc3xa8me_dextension_de_Carathxc3xa9odory.
- Carathxc3xa9odorys_extension_theorem sameAs משפט_ההרחבה_של_קרתאודורי.
- Carathxc3xa9odorys_extension_theorem sameAs カラテオドリの拡張定理.
- Carathxc3xa9odorys_extension_theorem sameAs m.0bd6nj.
- Carathxc3xa9odorys_extension_theorem sameAs Теорема_Каратеодори_о_продолжении_меры.
- Carathxc3xa9odorys_extension_theorem sameAs Теорема_Каратеодорі_про_продовження_міри.
- Carathxc3xa9odorys_extension_theorem sameAs Q2631152.
- Carathxc3xa9odorys_extension_theorem sameAs Q2631152.
- Carathxc3xa9odorys_extension_theorem wasDerivedFrom Carathxc3xa9odorys_extension_theoremoldid=625355493.
- Carathxc3xa9odorys_extension_theorem isPrimaryTopicOf Carathxc3xa9odorys_extension_theorem.