Both actually! See section 6 in Making Ado Without Expectations—unmeasurable sets are one kind of expectation gap (6.2.1) and ‘single-hit’ infinities are another (6.1.2)
When would you need to deal with unmeasurable sets in practice? They can’t be constructed explicitly, i.e. with just ZF without the axiom of choice, at least for the Lebesgue measure on the real numbers (and I assume this extends to Rn, but I don’t know about infinite-dimensional spaces). I don’t think they’re a problem.
You’re correct, in practice you wouldn’t—that’s the ‘instrumentalist’ point made in the latter half of the post
Both actually! See section 6 in Making Ado Without Expectations—unmeasurable sets are one kind of expectation gap (6.2.1) and ‘single-hit’ infinities are another (6.1.2)
When would you need to deal with unmeasurable sets in practice? They can’t be constructed explicitly, i.e. with just ZF without the axiom of choice, at least for the Lebesgue measure on the real numbers (and I assume this extends to Rn, but I don’t know about infinite-dimensional spaces). I don’t think they’re a problem.
You’re correct, in practice you wouldn’t—that’s the ‘instrumentalist’ point made in the latter half of the post