Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Borel_set> ?p ?o }
- 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.".
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- Borel_set wikiPageWikiLink Alexander_S._Kechris.
- Borel_set wikiPageWikiLink Analytic_set.
- Borel_set wikiPageWikiLink Baire_set.
- Borel_set wikiPageWikiLink Borel_hierarchy.
- Borel_set wikiPageWikiLink Borel_measure.
- Borel_set wikiPageWikiLink Cardinality.
- Borel_set wikiPageWikiLink Cardinality_of_the_continuum.
- Borel_set wikiPageWikiLink Category:Descriptive_set_theory.
- Borel_set wikiPageWikiLink Category:Topology.
- Borel_set wikiPageWikiLink Category_(mathematics).
- Borel_set wikiPageWikiLink Closed_set.
- Borel_set wikiPageWikiLink Compact_space.
- Borel_set wikiPageWikiLink Complement_(set_theory).
- Borel_set wikiPageWikiLink Continued_fraction.
- Borel_set wikiPageWikiLink Countable_set.
- Borel_set wikiPageWikiLink Cylindrical_σ-algebra.
- Borel_set wikiPageWikiLink Descriptive_set_theory.
- Borel_set wikiPageWikiLink Divisor.
- Borel_set wikiPageWikiLink First_uncountable_ordinal.
- Borel_set wikiPageWikiLink George_Mackey.
- Borel_set wikiPageWikiLink Halsey_Royden.
- Borel_set wikiPageWikiLink Hausdorff_space.
- Borel_set wikiPageWikiLink Integer.
- Borel_set wikiPageWikiLink Intersection_(set_theory).
- Borel_set wikiPageWikiLink Interval_(mathematics).
- Borel_set wikiPageWikiLink Irrational_number.
- Borel_set wikiPageWikiLink Isomorphism.
- Borel_set wikiPageWikiLink Limit_ordinal.
- Borel_set wikiPageWikiLink Maharams_theorem.
- Borel_set wikiPageWikiLink Mathematics.
- Borel_set wikiPageWikiLink Measurable_function.
- Borel_set wikiPageWikiLink Measure_(mathematics).
- Borel_set wikiPageWikiLink Metric_(mathematics).
- Borel_set wikiPageWikiLink Metric_space.
- Borel_set wikiPageWikiLink Mizar_system.
- Borel_set wikiPageWikiLink Morphism.
- Borel_set wikiPageWikiLink Nikolai_Luzin.
- Borel_set wikiPageWikiLink Non-measurable_set.
- Borel_set wikiPageWikiLink Open_set.
- Borel_set wikiPageWikiLink Ordinal_number.
- Borel_set wikiPageWikiLink Parity_function.
- Borel_set wikiPageWikiLink Pathological_(mathematics).
- Borel_set wikiPageWikiLink Paul_Halmos.
- Borel_set wikiPageWikiLink Polish_space.
- Borel_set wikiPageWikiLink Power_set.
- Borel_set wikiPageWikiLink Probability_distribution.
- Borel_set wikiPageWikiLink Probability_measure.
- Borel_set wikiPageWikiLink Probability_space.
- Borel_set wikiPageWikiLink Probability_theory.
- Borel_set wikiPageWikiLink Pullback.
- Borel_set wikiPageWikiLink Real_number.
- Borel_set wikiPageWikiLink Richard_M._Dudley.
- Borel_set wikiPageWikiLink Saturated_set.
- Borel_set wikiPageWikiLink Second-countable_space.
- Borel_set wikiPageWikiLink Separable_space.
- Borel_set wikiPageWikiLink Sigma-algebra.
- Borel_set wikiPageWikiLink Sigma-ring.
- Borel_set wikiPageWikiLink Standard_probability_space.
- Borel_set wikiPageWikiLink Subsequence.
- Borel_set wikiPageWikiLink Topological_space.
- Borel_set wikiPageWikiLink Transfinite_induction.
- Borel_set wikiPageWikiLink Union_(set_theory).
- Borel_set wikiPageWikiLink William_Arveson.
- Borel_set wikiPageWikiLink Émile_Borel.
- Borel_set wikiPageWikiLink Σ-compact_space.
- Borel_set wikiPageWikiLinkText "Borel set".
- Borel_set wikiPageWikiLinkText "Borel set#Non-Borel sets".
- Borel_set wikiPageWikiLinkText "Borel set#Standard Borel spaces and Kuratowski theorems".
- Borel_set wikiPageWikiLinkText "Borel space".
- Borel_set wikiPageWikiLinkText "Borel structure".
- Borel_set wikiPageWikiLinkText "Borel subset".
- Borel_set wikiPageWikiLinkText "Borel subsets".
- Borel_set wikiPageWikiLinkText "Borel σ-algebra".
- Borel_set wikiPageWikiLinkText "Borel".
- Borel_set wikiPageWikiLinkText "Non-Borel sets".
- Borel_set wikiPageWikiLinkText "set".
- Borel_set wikiPageWikiLinkText "standard Borel space".
- Borel_set id "BorelSet".
- Borel_set id "p/b017120".
- Borel_set title "Borel Set".
- Borel_set title "Borel set".
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- Borel_set subject Category:Descriptive_set_theory.
- Borel_set subject Category:Topology.
- Borel_set type Diacritic.
- Borel_set type Field.
- Borel_set type Redirect.
- 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.".