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.
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