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- In mathematics, more specifically in measure theory, the Baire sets form a σ-algebra of a topological space that avoids some of the pathological properties of Borel sets. There are several inequivalent definitions of Baire sets, but in the most widely used, the Baire sets of a locally compact Hausdorff space form the smallest σ-algebra such that all compactly supported continuous functions are measurable. Thus, measures defined on this σ-algebra, called Baire measures, are a convenient framework for integration on locally compact Hausdorff spaces. In particular, any compactly supported continuous function on such a space is integrable with respect to any finite Baire measure. Every Baire set is a Borel set. The converse holds in many, but not all, topological spaces. Baire sets 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 sets were introduced by Kunihiko Kodaira , Shizuo Kakutani and Kunihiko Kodaira and Halmos , who named them after Baire functions, which are in turn named after René-Louis Baire. (en)
- 측도론에서 베르 집합(Baire集合, 영어: Baire set)은 실수 값 연속 함수들을 모두 가측 함수로 만드는 가장 엉성한 시그마 대수이다. 구체적으로, Gδ 콤팩트 집합들로 생성된다. 베르 집합들의 시그마 대수는 보렐 시그마 대수의 부분 시그마 대수이다. (ko)
- 数学、特に測度論においてベール集合は測度論と位相空間論の関係の理解に重要な概念である。とくに、ベール集合の理解は距離付不能な位相空間での測度の扱いに関する直観を助ける。ベール集合はボレル集合のサブクラスである。逆も全てではないが多くの重要な位相空間で成り立つ。 (ja)
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- 9049 (xsd:nonNegativeInteger)
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- Kunihiko (en)
- Shizuo (en)
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- Kodaira (en)
- Kakutani (en)
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- 1941 (xsd:integer)
- 1944 (xsd:integer)
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| rdfs:comment
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- 측도론에서 베르 집합(Baire集合, 영어: Baire set)은 실수 값 연속 함수들을 모두 가측 함수로 만드는 가장 엉성한 시그마 대수이다. 구체적으로, Gδ 콤팩트 집합들로 생성된다. 베르 집합들의 시그마 대수는 보렐 시그마 대수의 부분 시그마 대수이다. (ko)
- 数学、特に測度論においてベール集合は測度論と位相空間論の関係の理解に重要な概念である。とくに、ベール集合の理解は距離付不能な位相空間での測度の扱いに関する直観を助ける。ベール集合はボレル集合のサブクラスである。逆も全てではないが多くの重要な位相空間で成り立つ。 (ja)
- In mathematics, more specifically in measure theory, the Baire sets form a σ-algebra of a topological space that avoids some of the pathological properties of Borel sets. There are several inequivalent definitions of Baire sets, but in the most widely used, the Baire sets of a locally compact Hausdorff space form the smallest σ-algebra such that all compactly supported continuous functions are measurable. Thus, measures defined on this σ-algebra, called Baire measures, are a convenient framework for integration on locally compact Hausdorff spaces. In particular, any compactly supported continuous function on such a space is integrable with respect to any finite Baire measure. (en)
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- Baire set (en)
- ベール集合 (ja)
- 베르 집합 (ko)
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