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- Sigma-ring abstract "In mathematics, a nonempty collection of sets is called a σ-ring (pronounced sigma-ring) if it is closed under countable union and relative complementation:if for all if From these two properties we immediately see thatif for all This is simply because .If the first property is weakened to closure under finite union (i.e., whenever ) but not countable union, then is a ring but not a σ-ring.σ-rings can be used instead of σ-fields in the development of measure and integration theory, if one does not wish to require that the universal set be measurable. Every σ-field is also a σ-ring, but a σ-ring need not be a σ-field.A σ-ring induces a σ-field. If is a σ-ring over the set , then define to be the collection of all subsets of X that are elements of or whose complements are elements of . We see that is a σ-field over the setX.".
- Sigma-ring wikiPageID "6928351".
- Sigma-ring wikiPageRevisionID "541268444".
- Sigma-ring hasPhotoCollection Sigma-ring.
- Sigma-ring subject Category:Measure_theory.
- Sigma-ring subject Category:Set_families.
- Sigma-ring type Abstraction100002137.
- Sigma-ring type Family108078020.
- Sigma-ring type Group100031264.
- Sigma-ring type Organization108008335.
- Sigma-ring type SetFamilies.
- Sigma-ring type SocialGroup107950920.
- Sigma-ring type Unit108189659.
- Sigma-ring type YagoLegalActor.
- Sigma-ring type YagoLegalActorGeo.
- Sigma-ring type YagoPermanentlyLocatedEntity.
- Sigma-ring comment "In mathematics, a nonempty collection of sets is called a σ-ring (pronounced sigma-ring) if it is closed under countable union and relative complementation:if for all if From these two properties we immediately see thatif for all This is simply because .If the first property is weakened to closure under finite union (i.e., whenever ) but not countable union, then is a ring but not a σ-ring.σ-rings can be used instead of σ-fields in the development of measure and integration theory, if one does not wish to require that the universal set be measurable. ".
- Sigma-ring label "Sigma-anneau".
- Sigma-ring label "Sigma-ring".
- Sigma-ring label "Σ-pierścień".
- Sigma-ring label "Σ集合環".
- Sigma-ring sameAs Sigma_okruh.
- Sigma-ring sameAs Sigma-anneau.
- Sigma-ring sameAs Σ集合環.
- Sigma-ring sameAs Σ-pierścień.
- Sigma-ring sameAs m.0gxh7s.
- Sigma-ring sameAs Q3123369.
- Sigma-ring sameAs Q3123369.
- Sigma-ring sameAs Sigma-ring.
- Sigma-ring wasDerivedFrom Sigma-ring?oldid=541268444.
- Sigma-ring isPrimaryTopicOf Sigma-ring.