Timeline for measure spaces as presheaves?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 30, 2009 at 20:20 | vote | accept | Zev Chonoles | ||
| Dec 2, 2009 at 11:35 | |||||
| Nov 30, 2009 at 17:59 | comment | added | Zev Chonoles | Thanks for the helpful explanation and links - it sounds like this is the right way to go. | |
| Nov 30, 2009 at 17:48 | vote | accept | Zev Chonoles | ||
| Nov 30, 2009 at 20:20 | |||||
| Nov 30, 2009 at 11:08 | history | edited | Konstantin Slutsky | CC BY-SA 2.5 |
added 516 characters in body
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| Nov 30, 2009 at 10:37 | comment | added | Konstantin Slutsky | OK, I had to be more precise. Measure, even if it can have infinite values, is always defined on clopen subsets of the Stone space. It is sigma additive in the following sense. If you have a disjoint sequence of clopen sets $a_i$ and if $a$ is the smallest clopen set that contains all $a_i$'s then measure of this $a$ is the sum of measures of $a_i$. This is just because of isomorphism between Boolean algebras. You can then, probably (I didn't check this), apply Caratheodory construction to get a measure on the Stone space. | |
| Nov 30, 2009 at 10:02 | comment | added | Harry Gindi | If we allow $\mu$ to take on infinite values, won't we run into some trouble trying to recover the $\sigma$-additivity? | |
| Nov 30, 2009 at 9:15 | history | answered | Konstantin Slutsky | CC BY-SA 2.5 |