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- Baire_set abstract "In mathematics, more specifically in measure theory, the Baire sets of a locally compact Hausdorff space form a σ-algebra related to the continuous functions on the space. There are several inequivalent definitions of Baire set, which all coincide for the case of locally compact σ-compact Hausdorff spaces.The Baire sets form a subclass of the Borel sets. The converse holds in many, but not all, topological spaces.Baire sets were introduced by Kunihiko Kodaira (1941, Definition 4), Shizuo Kakutani and Kunihiko Kodaira (1944) and Halmos (1950, page 220), who named them after Baire functions that are in turn named after René-Louis Baire. They introduced them to avoid some pathological properties of Borel sets on spaces without a countable base for the topology. In practice, the use of Baire measures on Baire sets can often be replaced by the use of regular Borel measures on Borel sets.".
- Baire_set wikiPageID "3976202".
- Baire_set wikiPageLength "8192".
- Baire_set wikiPageOutDegree "27".
- Baire_set wikiPageRevisionID "669345809".
- Baire_set wikiPageWikiLink Baire_function.
- Baire_set wikiPageWikiLink Borel_set.
- Baire_set wikiPageWikiLink Category:General_topology.
- Baire_set wikiPageWikiLink Category:Measure_theory.
- Baire_set wikiPageWikiLink Compact_space.
- Baire_set wikiPageWikiLink Complete_measure.
- Baire_set wikiPageWikiLink Continuous_function.
- Baire_set wikiPageWikiLink Countable_set.
- Baire_set wikiPageWikiLink Discrete_space.
- Baire_set wikiPageWikiLink Discrete_topological_space.
- Baire_set wikiPageWikiLink Euclidean_space.
- Baire_set wikiPageWikiLink G-delta_set.
- Baire_set wikiPageWikiLink Gδ_set.
- Baire_set wikiPageWikiLink Hausdorff_space.
- Baire_set wikiPageWikiLink Kolmogorov_extension_theorem.
- Baire_set wikiPageWikiLink Kunihiko_Kodaira.
- Baire_set wikiPageWikiLink Locally_compact.
- Baire_set wikiPageWikiLink Locally_compact_space.
- Baire_set wikiPageWikiLink Mathematics.
- Baire_set wikiPageWikiLink Measure_(mathematics).
- Baire_set wikiPageWikiLink Measure_theory.
- Baire_set wikiPageWikiLink Regular_measure.
- Baire_set wikiPageWikiLink René-Louis_Baire.
- Baire_set wikiPageWikiLink Sigma-algebra.
- Baire_set wikiPageWikiLink Sigma-ring.
- Baire_set wikiPageWikiLink Sigma_ring.
- Baire_set wikiPageWikiLink Standard_probability_space.
- Baire_set wikiPageWikiLink Σ-algebra.
- Baire_set wikiPageWikiLinkText "Baire set".
- Baire_set first "Kunihiko".
- Baire_set first "Shizuo".
- Baire_set hasPhotoCollection Baire_set.
- Baire_set last "Kakutani".
- Baire_set last "Kodaira".
- Baire_set loc "Definition 4".
- Baire_set wikiPageUsesTemplate Template:Citation.
- Baire_set wikiPageUsesTemplate Template:Cite_book.
- Baire_set wikiPageUsesTemplate Template:For.
- Baire_set wikiPageUsesTemplate Template:Harv.
- Baire_set wikiPageUsesTemplate Template:Harvs.
- Baire_set wikiPageUsesTemplate Template:Harvtxt.
- Baire_set year "1941".
- Baire_set year "1944".
- Baire_set subject Category:General_topology.
- Baire_set subject Category:Measure_theory.
- Baire_set comment "In mathematics, more specifically in measure theory, the Baire sets of a locally compact Hausdorff space form a σ-algebra related to the continuous functions on the space. There are several inequivalent definitions of Baire set, which all coincide for the case of locally compact σ-compact Hausdorff spaces.The Baire sets form a subclass of the Borel sets.".
- Baire_set label "Baire set".
- Baire_set sameAs ベール集合.
- Baire_set sameAs m.0117vm09.
- Baire_set sameAs Q4848630.
- Baire_set sameAs Q4848630.
- Baire_set wasDerivedFrom Baire_set?oldid=669345809.
- Baire_set isPrimaryTopicOf Baire_set.