About: Decomposable measure

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In mathematics, a decomposable measure (also known as a strictly localizable measure) is a measure that is a disjoint union of finite measures. This is a generalization of σ-finite measures, which are the same as those that are a disjoint union of countably many finite measures. There are several theorems in measure theory such as the Radon–Nikodym theorem that are not true for arbitrary measures but are true for σ-finite measures. Several such theorems remain true for the more general class of decomposable measures. This extra generality is not used much as most decomposable measures that occur in practice are σ-finite.

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  • In mathematics, a decomposable measure (also known as a strictly localizable measure) is a measure that is a disjoint union of finite measures. This is a generalization of σ-finite measures, which are the same as those that are a disjoint union of countably many finite measures. There are several theorems in measure theory such as the Radon–Nikodym theorem that are not true for arbitrary measures but are true for σ-finite measures. Several such theorems remain true for the more general class of decomposable measures. This extra generality is not used much as most decomposable measures that occur in practice are σ-finite. (en)
  • 数学において分解可能測度（ぶんかいかのうそくど、英: decomposable measure）とは、の直和であるような測度のことを言う。可算個の測度の直和であるような の一般化である。ラドン＝ニコディムの定理のように、σ-有限測度に対しては真となるが任意の測度に対しては真とならない定理が測度論にはいくつか存在する。そのような定理のいくつかは、より一般の分解可能測度の類に対しても真となる。しかし、実践上現れる分解可能測度のほとんどは σ-有限であるため、このような一般化はあまり用いられない。 (ja)
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  • In mathematics, a decomposable measure (also known as a strictly localizable measure) is a measure that is a disjoint union of finite measures. This is a generalization of σ-finite measures, which are the same as those that are a disjoint union of countably many finite measures. There are several theorems in measure theory such as the Radon–Nikodym theorem that are not true for arbitrary measures but are true for σ-finite measures. Several such theorems remain true for the more general class of decomposable measures. This extra generality is not used much as most decomposable measures that occur in practice are σ-finite. (en)
  • 数学において分解可能測度（ぶんかいかのうそくど、英: decomposable measure）とは、の直和であるような測度のことを言う。可算個の測度の直和であるような の一般化である。ラドン＝ニコディムの定理のように、σ-有限測度に対しては真となるが任意の測度に対しては真とならない定理が測度論にはいくつか存在する。そのような定理のいくつかは、より一般の分解可能測度の類に対しても真となる。しかし、実践上現れる分解可能測度のほとんどは σ-有限であるため、このような一般化はあまり用いられない。 (ja)
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  • Decomposable measure (en)
  • 分解可能測度 (ja)
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