Timeline for Understanding measure-preserving transformation [closed]
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 12, 2018 at 7:15 | history | closed |
David Handelman Chris Godsil Ben McKay Stefan Kohl♦ Stefan Waldmann |
Not suitable for this site | |
| Mar 10, 2018 at 8:17 | vote | accept | Jokerr | ||
| Mar 9, 2018 at 22:27 | comment | added | Gerald Edgar | When $\phi$ is bijective, your definition is fine. But if $\phi$ is not injective it is not what you want. A nice measure-preserving map is $x \mapsto (2x \;\mathrm{ mod }\; 1)$ on $[0,1)$ with Lebesgue measure. This satisfies the correct definition, but not yours. | |
| Mar 9, 2018 at 21:31 | comment | added | D. Thomine | See also this Math.Stackexchange thread: math.stackexchange.com/questions/1768257/… | |
| Mar 9, 2018 at 21:19 | comment | added | Johannes Hahn | For one thing, $\mu(\phi(A))$ isn't even defined in general. | |
| Mar 9, 2018 at 20:23 | review | Close votes | |||
| Mar 12, 2018 at 7:15 | |||||
| Mar 9, 2018 at 20:18 | answer | added | Iosif Pinelis | timeline score: 3 | |
| Mar 9, 2018 at 19:45 | comment | added | LSpice | Suppose that $S = \{a, b\}$, with $\mu(a) = 0$ and $\mu(b) = 1$. Then the constant function at $b$ is measure-preserving, but doesn't satisfy your definition. | |
| Mar 9, 2018 at 19:43 | review | First posts | |||
| Mar 9, 2018 at 20:04 | |||||
| Mar 9, 2018 at 19:32 | history | asked | Jokerr | CC BY-SA 3.0 |