History of Borel measure

	Revision 3 . . December 14, 2001 2:21 pm by AxelBoldt
	Revision 2 . . (edit) October 29, 2001 6:32 am by Hagedis [links]

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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.