Timeline for Why do probabilists take random variables to be Borel (and not Lebesgue) measurable?
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| Aug 24, 2019 at 3:27 | history | edited | Yuval Peres | CC BY-SA 4.0 |
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| Jul 17, 2010 at 19:43 | comment | added | Terry Tao | This is also a reason why the Borel sigma algebra on the domain is often preferred in ergodic theory. (A closely related reason is because of the connection between ergodic theory and topological dynamics; a topological dynamical system has a canonical Borel sigma algebra but not a canonical Lebesgue sigma algebra.) On the other hand, a significant portion of ergodic theory is also concerned with almost everywhere convergence (wrt some reference invariant measure, of course), and then it becomes useful for the domain sigma algebra to be complete... | |
| Jul 17, 2010 at 4:50 | history | answered | Yuval Peres | CC BY-SA 2.5 |