Timeline for Continuous relations?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 25, 2014 at 17:47 | comment | added | Qfwfq | Ok, thank you for the explanations! | |
| Aug 25, 2014 at 15:54 | comment | added | Nik Weaver | They can be converted to set-theoretic relations in general, see Section 1.3 of my paper. (But IMHO that is not a particularly good or helpful way to think about them.) | |
| Aug 25, 2014 at 13:32 | comment | added | Qfwfq | Ok, so in the case of the counting measure you have an underlying (set theoretic) relation $R\subseteq X\times Y$. But what about more general measures? | |
| Aug 24, 2014 at 23:09 | comment | added | Nik Weaver | @Qfwfq: No. In the case of counting measure, my definition is equivalent to having a subset of $X \times Y$. (Given $r \subseteq X \times Y$, let $(A,B) \in R$ iff $(x,y) \in r$ for some $x \in A$ and $y \in B$. This is a measurable relation and every measurable relation arises in this way.) | |
| Aug 24, 2014 at 22:35 | comment | added | Qfwfq | Maybe I've missed the point of the definition, but isn't it a notion of "measurable relation between measurable subsets" ($R\subseteq P(X)\times P(Y)$) rather than just a "measuranle relation between elements" ($R\subseteq X\times Y$)? | |
| Aug 23, 2014 at 17:54 | comment | added | Nik Weaver | Sure, I just meant that the question was posed very broadly. Thanks for the compliment! | |
| Aug 23, 2014 at 17:38 | comment | added | Lehs | I don't request for cool ideas, but for a good extension. Your idea is related and interesting. | |
| Aug 23, 2014 at 17:11 | history | answered | Nik Weaver | CC BY-SA 3.0 |