Talk:Regular measure
 | The contents of the Inner regular measure page were merged into Regular measure on 10 September 2024. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
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Compact sets
editI have seen a definition where the closed set is required to be compact.
- Also I see such a definition. Thus I correct the article. Boris Tsirelson (talk) 20:23, 25 April 2009 (UTC)
The two definitions of -regular set given in the article are only equivalent if the set has finite measure. Dvtausk (talk) 23:56, 27 August 2011 (UTC)
On any metric space?
editIn Section "Examples" it is written:
- Any Borel probability measure on any metric space is a regular measure.
I am afraid, this is wrong. Every subset of [0,1] is naturally a (separable) metric space; if the subset is not Lebesgue measurable then it admits a Borel probability measure with no sigma-compact set of full measure; and moreover, it admits a Borel probability measure with no compact set of nonzero measure.
There are two ways to make it true. One way: switch to the definition with closed (rather than compact) sets. The other way: assume that the space is Polish.
Merge from Inner regular measure
editI slapped a mergeto template onto Inner regular measure mostly because that article says less about inner measures than this article does. The only nice thing that it does is to more carefully distinguish Borel sigma algebras from other, finer sigma algebras that are still compatible with the topology. Well, that, and it also defines "tight", and has some references missing in this article. 67.198.37.16 (talk) 05:12, 5 December 2023 (UTC)
Merger complete. Klbrain (talk) 19:03, 10 September 2024 (UTC)
