Talk:Borel measure

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[edit] Completion

The article states:

The Borel measure is not complete.

The article on complete measure states that completions are unique. What is the completion of the Borel measure (is it the Lebesgue measure)? linas 00:53, 23 November 2005 (UTC)

Yes— at least in the case of the real line that is how Lebesgue measure is defined. - Gauge 22:41, 22 January 2006 (UTC)

I have understood the term "Borel measure" to mean any measure on the sigma-algebra of Borel sets in a topological space. Does this jar with what others here have seen? Michael Hardy 21:54, 1 June 2006 (UTC)

I understand a "Borel measure" to be any measure on the Borel sigma-algebra which is finite on compact sets, so I would say that this article seems misleading and should be expanded. Madmath789 15:05, 17 June 2006 (UTC)

following up on comment by Michael Hardy: the requirement that compact sets have finite measure, along with the measure of a set can be approximated from above by those of open sets, are for "regular" measures, stronger than mere Borel. Mct mht 21:13, 18 June 2006 (UTC)