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- Radon–Nikodym_theorem abstract "In mathematics, the Radon–Nikodym theorem is a result in measure theory that states that, given a measurable space (X, Σ), if a σ-finite measure ν on (X, Σ) is absolutely continuous with respect to a σ-finite measure μ on (X, Σ), then there is a measurable function f : X → [0, ∞), such that for any measurable subset A ⊂ X:The function f is called the Radon–Nikodym derivative and denoted by dν/dμ.The theorem is named after Johann Radon, who proved the theorem for the special case where the underlying space is RN in 1913, and for Otto Nikodym who proved the general case in 1930. In 1936 Hans Freudenthal further generalized the Radon–Nikodym theorem by proving the Freudenthal spectral theorem, a result in Riesz space theory, which contains the Radon–Nikodym theorem as a special case.If Y is a Banach space and the generalization of the Radon–Nikodym theorem also holds for functions with values in Y (mutatis mutandis), then Y is said to have the Radon–Nikodym property. All Hilbert spaces have the Radon–Nikodym property.".
- Radon–Nikodym_theorem wikiPageID "338746".
- Radon–Nikodym_theorem wikiPageRevisionID "601277690".
- Radon–Nikodym_theorem id "3998".
- Radon–Nikodym_theorem title "Radon–Nikodym theorem".
- Radon–Nikodym_theorem subject Category:Articles_containing_proofs.
- Radon–Nikodym_theorem subject Category:Generalizations_of_the_derivative.
- Radon–Nikodym_theorem subject Category:Integral_representations.
- Radon–Nikodym_theorem subject Category:Theorems_in_measure_theory.
- Radon–Nikodym_theorem comment "In mathematics, the Radon–Nikodym theorem is a result in measure theory that states that, given a measurable space (X, Σ), if a σ-finite measure ν on (X, Σ) is absolutely continuous with respect to a σ-finite measure μ on (X, Σ), then there is a measurable function f : X → [0, ∞), such that for any measurable subset A ⊂ X:The function f is called the Radon–Nikodym derivative and denoted by dν/dμ.The theorem is named after Johann Radon, who proved the theorem for the special case where the underlying space is RN in 1913, and for Otto Nikodym who proved the general case in 1930. ".
- Radon–Nikodym_theorem label "Radon–Nikodym theorem".
- Radon–Nikodym_theorem label "Satz von Radon-Nikodým".
- Radon–Nikodym_theorem label "Teorema de Radon–Nikodym".
- Radon–Nikodym_theorem label "Teorema di Radon-Nikodym".
- Radon–Nikodym_theorem label "Théorème de Radon-Nikodym-Lebesgue".
- Radon–Nikodym_theorem label "Twierdzenie Radona-Nikodýma".
- Radon–Nikodym_theorem label "Теорема Радона — Никодима".
- Radon–Nikodym_theorem label "拉东-尼科迪姆定理".
- Radon–Nikodym_theorem sameAs Radon%E2%80%93Nikodym_theorem.
- Radon–Nikodym_theorem sameAs Satz_von_Radon-Nikodým.
- Radon–Nikodym_theorem sameAs Teorema_de_Radon–Nikodym.
- Radon–Nikodym_theorem sameAs Théorème_de_Radon-Nikodym-Lebesgue.
- Radon–Nikodym_theorem sameAs Teorema_di_Radon-Nikodym.
- Radon–Nikodym_theorem sameAs ラドン=ニコディムの定理.
- Radon–Nikodym_theorem sameAs 라돈-니코딤_정리.
- Radon–Nikodym_theorem sameAs Twierdzenie_Radona-Nikodýma.
- Radon–Nikodym_theorem sameAs Q1191319.
- Radon–Nikodym_theorem sameAs Q1191319.
- Radon–Nikodym_theorem wasDerivedFrom Radon–Nikodym_theorem?oldid=601277690.