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)
Famous quotes containing the word sets:
“Nothing sets a person up more than having something turn out just the way its supposed to be, like falling into a Swiss snowdrift and seeing a big dog come up with a little cask of brandy round its neck.”
—Claud Cockburn (19041981)