Set of real numbers that is not Lebesgue measurable
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.
^Vitali, Giuseppe (1905). "Sul problema della misura dei gruppi di punti di una retta". Bologna, Tip. Gamberini e Parmeggiani.
mathematics, a Vitaliset is an elementary example of a set of real numbers that is not Lebesgue measurable, found by Giuseppe Vitali in 1905. The Vitali theorem...
most notably the Vitaliset with which he was the first to give an example of a non-measurable subset of real numbers. Giuseppe Vitali was the eldest of...
Lebesgue-measurable. ZFC proves that non-measurable sets do exist; an example is the Vitalisets. The first part of the definition states that the subset...
functions, such as Vitali convergence theorem Vitali also proved the existence of non-measurable subsets of the real numbers, see Vitaliset This disambiguation...
to cover, up to a Lebesgue-negligible set, a given subset E of Rd by a disjoint family extracted from a Vitali covering of E. There are two basic versions...
organized crime was depicted in film and television,[citation needed] Vitaliset about creating his own TV series. Largely financed by his own money, the...
} In this topology, a set U {\displaystyle U} is a neighborhood of + ∞ {\displaystyle +\infty } if and only if it contains a set { x : x > a } {\displaystyle...
choice is not needed to well-order them. The following construction of the Vitaliset shows one way that the axiom of choice can be used in a proof by transfinite...
Кличко́ [wiˈtɑl⁽ʲ⁾ij woloˈdɪmɪrowɪtʃ klɪtʃˈkɔ]; born 19 July 1971), known as Vitali Klitschko, is a Ukrainian politician and former professional boxer. He serves...
there are sets of reals without the property of Baire. In particular, the Vitaliset does not have the property of Baire. Already weaker versions of choice...
"Vera" Vitali (born 3 October 1981) is a Swedish actress and playwright, who stars as Lisa in the drama series Bonus Family. Anna Vera Vitali was born...
Vitali, Vitalii, Vitaly, Vitaliy and may refer to: Vitaly Borker (born 1975 or 1976), Ukrainian American Internet fraudster and cyberbully Vitaly Churkin...
interval [0;1] has measure 1. There exist sets of real numbers that are not Lebesgue measurable, e.g. Vitalisets. The supremum axiom of the reals refers...
variation Radon–Nikodym theorem Fubini's theorem Double integral Vitaliset, non-measurable set Henstock–Kurzweil integral Amenable group Banach–Tarski paradox...
{\displaystyle A} is a non-measurable subset of the real line, such as the Vitaliset. Then the λ 2 {\displaystyle \lambda ^{2}} -measure of { 0 } × A {\displaystyle...
1, the representative sequences form a non-measurable set. (This set is similar to a Vitaliset, the only difference being that equivalence classes are...
f = 1 V − 1 2 , {\displaystyle f=1_{V}-{\frac {1}{2}},} where V is a Vitaliset, it is clear that f is not measurable, but its absolute value is, being...
Vitali Yuryevich Kravtsov (Russian: Виталий Юрьевич Кравцов, IPA: [vʲɪˈtalʲɪj ˈjʉrʲjɪvʲɪtɕ ˈkraftsəf]; born 23 December 1999) is a Russian professional...
ring in 2008 Vitali Klitschko was looking to make an eighth consecutive defence of his crown. Derek Chisora had been set to face Vitali's brother Wladimir...
Vitali (7 March 1663 – 9 May 1745) was an Italian composer and violinist of the mid to late Baroque era. The eldest son of Giovanni Battista Vitali,...
if and only if it is measurable, so for every such function there is a Vitaliset. The construction of f relies on the axiom of choice. This example can...
in G. Cosets of Q in R are used in the construction of Vitalisets, a type of non-measurable set. Cosets are central in the definition of the transfer...
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