Measure theory | Articles containing proofs | Sets of real numbers

Vitali set

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. The Vitali theorem is the existence theorem that there are such sets. There are uncountably many Vitali sets, and their existence depends on the axiom of choice. In 1970, Robert Solovay constructed a model of Zermelo–Fraenkel set theory without the axiom of choice where all sets of real numbers are Lebesgue measurable, assuming the existence of an inaccessible cardinal (see Solovay model). (Wikipedia).

Vitali set
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Set Theory (Part 2): ZFC Axioms

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From playlist Set Theory by Mathoma

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From playlist Set Theory

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From playlist Set Theory

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Powered by https://www.numerise.com/ Listing elements from a set (2)

From playlist Set theory

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From playlist Axiomatic Set Theory

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From playlist Set Theory by Mathoma

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From playlist Sets (Discrete Math)

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From playlist Mathematics

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Rest In Peace @vk_intel https://www.gofundme.com/f/vitali-kremez-community-memorial

From playlist Open Analysis Live!

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From playlist The New CHALKboard

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From playlist The CERIAS Security Seminars 2005 (1)

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From playlist Podcast

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From playlist Set Theory

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Choice Functions and Length: Why you can't measure everything you choose

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From playlist The New CHALKboard

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From playlist Brilliant Music

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From playlist Open Analysis Live!

Related pages

Lebesgue measure | Non-measurable set | Carathéodory's extension theorem | Solovay model | Uncountable set | Disjoint sets | Rational number | Existence theorem | Banach–Tarski paradox | Quotient group | Zermelo–Fraenkel set theory | Dense set | Mathematics | Addition | Partition of a set | Real number | Normal subgroup | Inaccessible cardinal | Giuseppe Vitali | Interval (mathematics) | Coset