Timeline for Invariant probability on a unit ball of a Banach space
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Mar 24, 2016 at 8:54 | vote | accept | user89292 | ||
| Mar 24, 2016 at 8:50 | history | edited | user89292 | CC BY-SA 3.0 |
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| Mar 23, 2016 at 8:58 | answer | added | Uri Bader | timeline score: 4 | |
| Mar 23, 2016 at 1:30 | comment | added | reuns | consider $B(x,\epsilon) \subset B_X$ the ball of radius $\epsilon$ around some $x \in B_X$. then $\mu(B(x,\epsilon)) = \mu(\gamma B(x,\epsilon)) = \mu( B(\gamma x,\epsilon))$ for any $\gamma \in \Gamma$. hence if $\Gamma$ is countably infinite, no, not even finitely supported. if $\Gamma$ is finite, there are the discrete distributions $H_{x_0}(x) = \sum_{\gamma \in \Gamma} \delta( x - \gamma x_0)$ where $x_0 \in B_X$ is fixed, from which (by filtering $\delta$ in some different directions on $B_X$) you can get some continuous distributions but only on a finite dimensional subset of $B_X$ | |
| Mar 22, 2016 at 16:24 | comment | added | Jean Duchon | 1°) What does strongly continuous mean for a discrete group action ? 2°) Would assuming $\Gamma=\mathbb Z$ be useful to you? | |
| Mar 22, 2016 at 13:14 | history | edited | user89292 | CC BY-SA 3.0 |
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| Mar 22, 2016 at 11:06 | comment | added | Benoît Kloeckner | A sufficient condition is that $\Gamma$ preserves a finite-dimensional subspace. If this is too trivial for your taste, consider replacing "non-atomic" by "not supported on a finite-dimensional subspace". | |
| Mar 22, 2016 at 10:27 | history | edited | YCor | CC BY-SA 3.0 |
added implicit assumption and changed tags
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| Mar 22, 2016 at 9:57 | comment | added | user89292 | oh, come on.... ;) | |
| Mar 22, 2016 at 9:30 | comment | added | Mikael de la Salle | The Dirac measure at $0$? | |
| Mar 22, 2016 at 9:29 | review | First posts | |||
| Mar 22, 2016 at 9:47 | |||||
| Mar 22, 2016 at 9:25 | history | asked | user89292 | CC BY-SA 3.0 |