Timeline for The set of all functions which vanish at infinity is a subset of the set of all functions which have vanishing variation
Current License: CC BY-SA 4.0
12 events
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| May 5, 2020 at 15:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 5, 2020 at 14:57 | vote | accept | Hussain Rashed | ||
| Apr 5, 2020 at 14:57 | |||||
| Apr 3, 2020 at 17:24 | comment | added | Zach Teitler | * For $f(x) = 1/(1+x^2)$, $\operatorname{Var}(f)(x) = \max\{1/(1+x^2), 1-1/(1+x^2)\}$ for all $x$, and the maximum is $1-1/(1+x^2)$ for $|x| \geq 1$. The point is the same though. | |
| Apr 3, 2020 at 14:37 | comment | added | Zach Teitler | At this point it may be a question for the authors. | |
| Apr 3, 2020 at 1:36 | comment | added | Hussain Rashed | I am reading this paper arxiv.org/pdf/1711.06836.pdf, and it stated on page 16 that $D_0(X)$ is a subset of $D_h(X)$, and that is not clear to me. | |
| Apr 3, 2020 at 1:22 | comment | added | Zach Teitler | Try an example: $X = E = \mathbb{R}$, $f(x) = 1/(1+x^2)$, so $\operatorname{Var}(f)(x) = 1 - 1/(1+x^2)$ for all $x$. Now whatever $K$ is, if $x \notin K$, then $\operatorname{Var}(f)|_{\mathbb{R}-K}(x)$ is still $1-1/(1+x^2)$. The problem is that you shouldn't just take all values $y$. You need to restrict to $y \in X-K$ as well. ... Can I ask you where this question came from? | |
| Apr 3, 2020 at 1:04 | history | edited | Hussain Rashed | CC BY-SA 4.0 |
added 43 characters in body
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| Apr 3, 2020 at 1:01 | comment | added | Hussain Rashed | $\operatorname{Var}_E(f)(x)$ where $x \in X-K$ is the largest distance between $f(x)$ and $f(y)$ where $(x,y)\in E$, while $\operatorname{Var}_E(f)|_{X-K}(x)$ is the largest distance between $f(x)$ and $f(y)$ where $(x,y)\in E \cap (X-K)\times (X-K)$. How would that help? | |
| Apr 3, 2020 at 0:03 | comment | added | Zach Teitler | Difference between $\operatorname{Var}(f)|_{X-K}$ and $\operatorname{Var}(f|_{X-K})$. | |
| Apr 2, 2020 at 20:48 | history | edited | Wlod AA | CC BY-SA 4.0 |
a nasty typo corrected
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| Apr 2, 2020 at 20:41 | history | edited | YCor | CC BY-SA 4.0 |
formatting, changed tag
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| Apr 2, 2020 at 20:21 | history | asked | Hussain Rashed | CC BY-SA 4.0 |