[lanstin]

Like the old joke: The axiom of choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?

But can you do stats without measure theory? Normal distribution in the limit and all that?

There is no linearly additive measure on rationals, and therefore no way to grab a rational uniformly from (0,1). Has to be skewed to some level of complexity in the denominator.