Borel measure
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In mathematics, the Borel algebra is the smallest σ-algebra on the real numbers R containing the intervals, and the Borel measure is the measure on this σ-algebra which gives to the interval [a, b] the measure b − a (where a < b).
The Borel measure is not complete, which is why in practice the complete Lebesgue measure is preferred: every Borel measurable set is also Lebesgue measurable, and the measures of the set agree.
In a more general (abstract) measure-theoretic context, Let E be a Hausdorff space. A measure μ on the σ-algbera <math>\mathfrak{B}(E) <math> (the Borel σ-algebra on E) is Borel iff <math>\mu(K) < +\infty\ \forall K \subset E<math> compact.