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:
“Music sets up ladders,
it makes us invisible,
it sets us apart,
it lets us escape;
but from the visible
there is no escape.”
—Hilda Doolittle (18861961)