Wikipedia: Borel measure

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The Borel measure is the measure on the smallest set algebra containing the
intervals which give to the interval [a,b] the measure b-a.

The Borel measure is the measure on the smallest sigma algebra containing the
intervals which gives to the interval [a, b] the measure b - a. 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.

The Borel measure is the measure on the smallest sigma algebra containing the intervals which gives to the interval [a, b] the measure b - a. 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.