# Talk:Outer measure

From Encyclopedia of Mathematics

I am rewriting this entry in User:Camillo.delellis/sandbox. Camillo (talk) 18:12, 20 September 2012 (CEST)

"Outer measures induced by measures": It seems, $\mathcal{H}$ is used but not defined. True,in the next phrase something is said about $\mathcal{H}$, but only in context of "some authors"; is the matter clear? Also: induced by measures? or by just set functions? --Boris Tsirelson (talk) 21:47, 20 September 2012 (CEST)

- In fact in a first version I had those two sentences swapped. Now it should be more clear. Indeed we could call the section
*Outer measures induced by set functions*. However this construction seems more commonly used when you have a $\nu$ which is already a measure or at least a finitely additive set function: the idea of the title is to draw the attention on the second point of Theorem 6. Camillo (talk) 22:00, 20 September 2012 (CEST)- But on the other hand, first, who defines outer measure induced by a
*measure*via*covers?*In this case, a much simpler definition is available. And second, Caratheodory construction does not start from a measure; and $\nu (A) = c_\alpha ({\rm diam}\, (A))^\alpha$ is not a measure. --Boris Tsirelson (talk) 07:45, 21 September 2012 (CEST)

- But on the other hand, first, who defines outer measure induced by a

"Remark 9": The Hausdorff measure, is it a measure or an outer measure? Later, in "Examples", it is claimed to be an outer measure; really? --Boris Tsirelson (talk) 21:53, 20 September 2012 (CEST)

**How to Cite This Entry:**

Outer measure.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Outer_measure&oldid=28081