Timeline for On measurability in Wiener space
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 31, 2018 at 19:07 | comment | added | Nate Eldredge | Classical Wiener measure, on the space of continuous functions, is defined on the Borel $\sigma$-algebra (or its completion). And every continuous function is measurable with respect to the Borel $\sigma$-algebra. This is completely trivial and there really are no details: under a continuous function, the preimage of every open set is open and hence Borel, so the function is measurable. | |
| Jul 31, 2018 at 19:03 | comment | added | Arnold Neumaier | @NateEldredge; Where can I find a detailed argument? I mean the sigma algebra with respect to which the Gaussian measure is defined. | |
| Jul 31, 2018 at 16:30 | comment | added | Nate Eldredge | If $f$ is continuous then it's certainly measurable, no further assumptions needed, assuming you mean measurable with respect to the Borel $\sigma$-algebra. Did you mean to write something else? | |
| Jul 31, 2018 at 16:24 | history | asked | Arnold Neumaier | CC BY-SA 4.0 |