In mathematics, a Vitali set is an elementary example of a set of real numbers that is not Lebesgue measurable, found by Giuseppe Vitali (1905). The Vitali theorem is the existence theorem that there are such sets. There are uncountably many Vitali sets, and their existence is proven on the assumption of the axiom of choice.
Read more about Vitali Set: Measurable Sets, Construction and Proof
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“To find the length of an object, we have to perform certain
physical operations. The concept of length is therefore fixed when the operations by which length is measured are fixed: that is, the concept of length involves as much as and nothing more than the set of operations by which length is determined.”
—Percy W. Bridgman (1882–1961)
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