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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 wikiPageRevisionID "604128177".
- 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 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 label "ベール集合".
- 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=604128177.
- Baire_set isPrimaryTopicOf Baire_set.