Borel measure

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(mathematical analysis) A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space.

日本語の意味

局所コンパクトハウスドルフ空間のBorel σ-代数上で定義された測度。

英語の意味

(mathematical analysis) A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space.

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We integrated the continuous function against a Borel measure to analyze its distribution on the locally compact Hausdorff space.

局所コンパクトハウスドルフ空間上の連続関数をボレル測度に対して積分し、その分布を解析した。

詳細

意味（1）

(mathematical analysis) A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space.

{{quote-book|en|author=Gerald B. Folland|title=Real Analysis: Modern Techniques and Their Applications| edition=Second| location=New York| publisher=John Wiley & Sons, Inc.| year=1999| section=§1.5| page=33| isbn=978-0-471-31716-6| oclc=803988029| text=We are now in a position to construct a definitive theory for measuring subsets of ℝ based on the idea that the measure of an interval is its length. We begin with a more general (but only slightly more complicated) construction that yields a large family of measures on ℝ whose domain is the Borel σ-algebra ℬ_ℝ; such measures are called Borel measures on ℝ.}}

詳細

Borel measures （ plural ）