Several results (e.g in probability theory or using prob. theory) are stated in an almost surely phrasing (meaning the set of outcomes where this is not so has measure zero)
How can one pass from such statements to the surely mode of such a result?
For example it is kown that some results that hold almost surely hold surely as well (or is strogly conjecture to be the case).
Can one go from the one to the other and if so what additional conditions would be needed?
As mentioned in the comments a suggestion is that if an almost sure result holds under any possible choice of measure could this imply => sure, since it would not make any practical difference for any measure choice. Sth along these lines..
Is this correct and if so, can this be formalized?