Non-measurable Sets
If the axiom of choice is assumed to be true, not all subsets of Euclidean space are Lebesgue measurable; examples of such sets include the Vitali set, and the non-measurable sets postulated by the Hausdorff paradox and the Banach–Tarski paradox.
Read more about this topic: Measure (mathematics)
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““Yes” shuts us in. “No” sets us free.”
—Mason Cooley (b. 1927)