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Uniqueness
editI've added a sentence to the lead saying Up to isomorphism, there is only one nontrivial standard Borel space. I don't expect it to stay that way, but I think it's OK for an article at this level of completeness.
What needs to be clarified is what I mean by nontrivial (answer: the countable ones are all trivial, because they correspond to the discrete topology and make all sets Borel; that may be too chatty for the lead). And most importantly, it should be sourced.
I would be very grateful to anyone who can find a source for the phrase "the standard Borel space", meaning the unique uncountable one. I have definitely encountered this usage, but I'm not sure where to find a print source. --Trovatore (talk) 21:12, 11 July 2017 (UTC)