# Borel measure

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 ba (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 [itex]\mathfrak{B}(E) [itex] (the Borel σ-algebra on E) is Borel iff [itex]\mu(K) < +\infty\ \forall K \subset E[itex] compact.

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy