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- Baire_measure abstract "In mathematics, a Baire measure is a measure on the σ-algebra of Baire sets of a topological space whose value on every compact Baire set is finite. In compact metric spaces the Borel sets and the Baire sets are the same, so Baire measures are the same as Borel measures that are finite on compact sets. In general Baire sets and Borel sets need not be the same. In this context, Baire measures are used because they connect to the properties of continuous functions more directly.There are several inequivalent definitions of Baire sets, so correspondingly there are several inequivalent concepts of Baire measure on a topological space. These all coincide on spaces that are locally compact σ-compact Hausdorff spaces. In practice Baire measures can be replaced by regular Borel measures. The relation between Baire measures and regular Borel measures is as follows: The restriction of a finite Borel measure to the Baire sets is a Baire measure.A finite Baire measure on a compact space is always regular.A finite Baire measure on a compact space is the restriction of a unique regular Borel measure.On compact (or σ-compact) metric spaces, Borel sets are the same as Baire sets and Borel measures are the same as Baire measures.".
- Baire_measure wikiPageID "13520509".
- Baire_measure wikiPageLength "1976".
- Baire_measure wikiPageOutDegree "23".
- Baire_measure wikiPageRevisionID "621697374".
- Baire_measure wikiPageWikiLink Abelian_group.
- Baire_measure wikiPageWikiLink Baire_set.
- Baire_measure wikiPageWikiLink Borel_measure.
- Baire_measure wikiPageWikiLink Borel_set.
- Baire_measure wikiPageWikiLink Category:Measures_(measure_theory).
- Baire_measure wikiPageWikiLink Compact_set.
- Baire_measure wikiPageWikiLink Compact_space.
- Baire_measure wikiPageWikiLink Continuous_function.
- Baire_measure wikiPageWikiLink Counting_measure.
- Baire_measure wikiPageWikiLink Haar_Measure.
- Baire_measure wikiPageWikiLink Haar_measure.
- Baire_measure wikiPageWikiLink Hausdorff_space.
- Baire_measure wikiPageWikiLink Hausdorff_spaces.
- Baire_measure wikiPageWikiLink Locally_compact_group.
- Baire_measure wikiPageWikiLink Measure_(mathematics).
- Baire_measure wikiPageWikiLink Metric_space.
- Baire_measure wikiPageWikiLink Metric_spaces.
- Baire_measure wikiPageWikiLink Meyer_Jerison.
- Baire_measure wikiPageWikiLink Pontryagin_duality.
- Baire_measure wikiPageWikiLink Regular_Borel_measure.
- Baire_measure wikiPageWikiLink Regular_measure.
- Baire_measure wikiPageWikiLink Sigma-algebra.
- Baire_measure wikiPageWikiLink Topological_space.
- Baire_measure wikiPageWikiLink Translation_invariant.
- Baire_measure wikiPageWikiLink Translational_symmetry.
- Baire_measure wikiPageWikiLink Unit_interval.
- Baire_measure wikiPageWikiLink Σ-algebra.
- Baire_measure wikiPageWikiLink Σ-compact.
- Baire_measure wikiPageWikiLink Σ-compact_space.
- Baire_measure wikiPageWikiLinkText "Baire measure".
- Baire_measure hasPhotoCollection Baire_measure.
- Baire_measure wikiPageUsesTemplate Template:Mathanalysis-stub.
- Baire_measure subject Category:Measures_(measure_theory).
- Baire_measure hypernym Measure.
- Baire_measure type Work.
- Baire_measure comment "In mathematics, a Baire measure is a measure on the σ-algebra of Baire sets of a topological space whose value on every compact Baire set is finite. In compact metric spaces the Borel sets and the Baire sets are the same, so Baire measures are the same as Borel measures that are finite on compact sets. In general Baire sets and Borel sets need not be the same.".
- Baire_measure label "Baire measure".
- Baire_measure sameAs Baire-maat.
- Baire_measure sameAs m.03c81j6.
- Baire_measure sameAs Q2577940.
- Baire_measure sameAs Q2577940.
- Baire_measure wasDerivedFrom Baire_measure?oldid=621697374.
- Baire_measure isPrimaryTopicOf Baire_measure.