Borel measure

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Borel measure

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After Emile Borel

Borel measure (plural Borel measures)

1. (mathematical analysis) A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space.
   • 1999, Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd edition, New York: John Wiley & Sons, Inc., →ISBN, →OCLC, §1.5, page 33:

     We are now in a position to construct a definitive theory for measuring subsets of ${\displaystyle \mathbb {R} }$ 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 ${\displaystyle \mathbb {R} }$ whose domain is the Borel σ-algebra ${\displaystyle {\mathcal {B}}_{\mathbb {R} }}$; such measures are called Borel measures on ${\displaystyle \mathbb {R} }$.