# 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

*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.