Timeline for Invariant probability on a unit ball of a Banach space
Current License: CC BY-SA 3.0
11 events
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| Mar 25, 2016 at 8:55 | comment | added | user89292 | That is very helpful, thanks again. | |
| Mar 24, 2016 at 11:02 | comment | added | Uri Bader | On the other hand, if you put assumptions on your measure classes you might get some non-trivial restrictions. For example, if your class is stationary (wrt a generating probability measure on $\Gamma$) then it already must be $\Gamma$-invariant (this follows from the metric-ergodicity of the Furstenberg-Poisson boundary). This puts you back in the setting of your question (and its answer). | |
| Mar 24, 2016 at 11:01 | comment | added | Uri Bader | Finding a probability measure whose class is invariant (even ergodic) is just too easy. For example you can find such a measure on $\Gamma$ itself (a positive summable to 1 function), fix a point $x\in X$ and push your measure via the orbit map. No assumption on the representation here. I suppose that there is no reasonable classification of invariant classes on $X$, even under strong assumptions on $X$ and the $\Gamma$-representation. | |
| Mar 24, 2016 at 10:52 | history | edited | Uri Bader | CC BY-SA 3.0 |
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| Mar 24, 2016 at 8:56 | comment | added | user89292 | by the way @user89334 do you have any idea if it is possible to find a probability measure whose class is preserved instead? | |
| Mar 24, 2016 at 8:54 | vote | accept | user89292 | ||
| Mar 24, 2016 at 8:17 | history | edited | Uri Bader | CC BY-SA 3.0 |
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| Mar 23, 2016 at 15:44 | history | edited | Uri Bader | CC BY-SA 3.0 |
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| Mar 23, 2016 at 15:38 | history | edited | Uri Bader | CC BY-SA 3.0 |
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| Mar 23, 2016 at 9:01 | review | First posts | |||
| Mar 23, 2016 at 9:05 | |||||
| Mar 23, 2016 at 8:58 | history | answered | Uri Bader | CC BY-SA 3.0 |