Borel measure

English

Etymology

After Emile Borel

Noun

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 $\mathbb {R}$ 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 $\mathbb {R}$ whose domain is the Borel σ-algebra ${\mathcal {B}}_{\mathbb {R} }$; such measures are called Borel measures on $\mathbb {R}$.

Translations

Translations

• Finnish: Borelin mitta, Borel-mitta
• German: Borel-Maß n
• Polish: miara borelowska f