Timeline for An ultrafilter and a partition
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Oct 30, 2010 at 23:02 | comment | added | Joel David Hamkins | Porton, I am just integrating the function $n\mapsto \mu_n(X)$ with respect to $\mu$. It amounts to the ultrapower of the $\mu_n$ by $\mu$, which can be thought of as a kind of integration, and this is why we use the $\int$ sign, but Andres is right that one can view it merely as a suggestive notation, falling back simply to the definition that was given. | |
| Oct 30, 2010 at 20:22 | comment | added | porton | In Wikipedia there is defined integral of a function. But Joel integrates a measure rather than a function. Where can I read about this? | |
| Oct 30, 2010 at 0:26 | comment | added | Andrés E. Caicedo | Porton: A decent book on measure theory should cover this, I would expect, though perhaps the examples there will be mostly non-atomic measures that are not 2-valued as in this case. (In particular, look at the Radon-Nikodym derivative, en.wikipedia.org/wiki/Radon%E2%80%93Nikodym_theorem) But the notation and the background prerequisites are a bit of a distraction here, Joel explicitly defined what it means for the case under consideration. | |
| Oct 29, 2010 at 22:03 | comment | added | porton | Where can I read a short introduction about such use of integral sign? | |
| Oct 29, 2010 at 4:58 | comment | added | Joel David Hamkins | This is the usual way of integrating measures with respect to a measure. We are adding up the $\mu_n$ values of the set $X$ with respect to the measure $\mu$. | |
| Oct 29, 2010 at 4:41 | comment | added | porton | Where you've got that usage of integral sign? | |
| Oct 29, 2010 at 4:25 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |