Saibal wrote:

>Bruno wrote: ''The probabilities are defined on infinite
>(continuous) set of infinite histories.''
>
>Isn't this in conflict with measure theory, because one would expect that 
>some 
>sets would be non-measurable?


No problem a priori, because the whole set can have some measure
although some subsets are not measurable.
So the situation is a priori similar to what happens with the reals.

Nevertheless I have just show that we must *isolate* a measure
from computability and provability theory (to solve the problem
of the origin of the physical law in the comp setting). And the
only technical steps I've done in that direction are rather modest 
(the isolation  of the Z logics). Those logics gives us just a 
hope for a "gleason theorem" in the computationalist realm.

Anyway, the fact that some subset of the set of all histories 
are non measurable is not relevant.

Existence or non existence of measurable sets can also
depends on choice or determinacy axioms. But this ultimately
depends on the Z (and Z*) logics. This would be premature.

Bruno

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