Difference between revisions of "Talk:Tight measure"
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"On a locally compact space $X$ such measures are also outer regular" – really? Even if the space is not separable, like (0,1) times a uncountable discrete space? --[[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 09:37, 30 November 2012 (CET) | "On a locally compact space $X$ such measures are also outer regular" – really? Even if the space is not separable, like (0,1) times a uncountable discrete space? --[[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 09:37, 30 November 2012 (CET) | ||
| + | :No, if the $\sigma$-algebra generated by the compact sets does not coincide with the Borel $\sigma$-algebra, then there are counterexamples. I missed that the references claiming this fact without assuming separability of the space assume anyway finiteness of the measure. [[User:Camillo.delellis|Camillo]] ([[User talk:Camillo.delellis|talk]]) 13:05, 30 November 2012 (CET) | ||
Latest revision as of 12:05, 30 November 2012
"On a locally compact space $X$ such measures are also outer regular" – really? Even if the space is not separable, like (0,1) times a uncountable discrete space? --Boris Tsirelson (talk) 09:37, 30 November 2012 (CET)
- No, if the $\sigma$-algebra generated by the compact sets does not coincide with the Borel $\sigma$-algebra, then there are counterexamples. I missed that the references claiming this fact without assuming separability of the space assume anyway finiteness of the measure. Camillo (talk) 13:05, 30 November 2012 (CET)
How to Cite This Entry:
Tight measure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tight_measure&oldid=28974
Tight measure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tight_measure&oldid=28974