Vitali set
Set of real numbers that is not Lebesgue measurable / From Wikipedia, the free encyclopedia
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In mathematics, a Vitali set is an elementary example of a set of real numbers that is not Lebesgue measurable, found by Giuseppe Vitali in 1905.[1] The Vitali theorem is the existence theorem that there are such sets. Each Vitali set is uncountable, and there are uncountably many Vitali sets. The proof of their existence depends on the axiom of choice.