Timeline for Non-Polish Lebesgue probability space?
Current License: CC BY-SA 3.0
6 events
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| Mar 1, 2014 at 12:27 | comment | added | R W | @timofei: Aha - I see. De la Rue (whom you apparently follow) uses the term "Lebesgue space" for something which is quite different from original Rokhlin's Lebesgue spaces (which are nowadays a part of the standard setup in ergodic theory). The point (and the principal advantage of Rokhlin's approach), once again, is that Rokhlin's definition is given in the measure category - there is not a single word about any topologies in this definition. | |
| Mar 1, 2014 at 11:13 | comment | added | timofei | user46855 this is very interesting. I think it answers my question but I have to check some details. | |
| Mar 1, 2014 at 11:00 | comment | added | timofei | R W: we have a set $X$ so we can speak of a topology on $X$. This is a good starting point for the theory of Lebesgue spaces, see Thierry de la Rue, Espaces de Lebesgue (numdam.org/numdam-bin/feuilleter?id=SPS_1993__27_). | |
| Mar 1, 2014 at 4:15 | comment | added | user46855 | Take the usual (Vitali) non-measurable subset of [0,1] with the (Caratheodory measurable sets for the) external Lebesgue measure. The measure is not compact (Pfangzagl Pierlo, compact systems of sets) lacking conditional probabilities, but measures on Polish spaces are compact. | |
| Mar 1, 2014 at 0:31 | comment | added | Nate Eldredge | It looks like there have been some edits that clarify the situation. | |
| Feb 28, 2014 at 22:42 | history | answered | R W | CC BY-SA 3.0 |