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- Borel_set abstract "In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named after Émile Borel.For a topological space X, the collection of all Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on X is the smallest σ-algebra containing all open sets (or, equivalently, all closed sets).Borel sets are important in measure theory, since any measure defined on the open sets of a space, or on the closed sets of a space, must also be defined on all Borel sets of that space. Any measure defined on the Borel sets is called a Borel measure. Borel sets and the associated Borel hierarchy also play a fundamental role in descriptive set theory.In some contexts, Borel sets are defined to be generated by the compact sets of the topological space, rather than the open sets. The two definitions are equivalent for many well-behaved spaces, including all Hausdorff σ-compact spaces, but can be different in more pathological spaces.".
- Borel_set wikiPageExternalLink emacs_search?input=(symbol+Borel_Sets+%7C+notation+%7C+constructor+%7C+occur+%7C+th)+ordered+by+number+of+ref.
- Borel_set wikiPageExternalLink K12.
- Borel_set wikiPageID "43327".
- Borel_set wikiPageRevisionID "602054291".
- Borel_set hasPhotoCollection Borel_set.
- Borel_set id "BorelSet".
- Borel_set id "p/b017120".
- Borel_set title "Borel Set".
- Borel_set title "Borel set".
- Borel_set subject Category:Descriptive_set_theory.
- Borel_set subject Category:Topology.
- Borel_set comment "In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named after Émile Borel.For a topological space X, the collection of all Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra.".
- Borel_set label "Algebra di Borel".
- Borel_set label "Borel set".
- Borel_set label "Borelsche σ-Algebra".
- Borel_set label "Borelstam".
- Borel_set label "Tribu borélienne".
- Borel_set label "Zbiór borelowski".
- Borel_set label "Álgebra de Borel".
- Borel_set label "Álgebra de Borel".
- Borel_set label "Борелевская сигма-алгебра".
- Borel_set label "ボレル集合".
- Borel_set label "博雷爾集".
- Borel_set sameAs Borelovská_množina.
- Borel_set sameAs Borelsche_σ-Algebra.
- Borel_set sameAs Álgebra_de_Borel.
- Borel_set sameAs Tribu_borélienne.
- Borel_set sameAs Algebra_di_Borel.
- Borel_set sameAs ボレル集合.
- Borel_set sameAs 보렐_집합.
- Borel_set sameAs Borelstam.
- Borel_set sameAs Zbiór_borelowski.
- Borel_set sameAs Álgebra_de_Borel.
- Borel_set sameAs m.0bw61.
- Borel_set sameAs Q1080067.
- Borel_set sameAs Q1080067.
- Borel_set wasDerivedFrom Borel_set?oldid=602054291.
- Borel_set isPrimaryTopicOf Borel_set.