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** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.

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Wikipedia

## Some Related Sentences

** and Vitali

** and theorem

__**__Tarski's

__theorem__: For every infinite set A,

**there**

**is**

**a**bijective map between

**the**

**sets**A and A × A

**.**

__**__König's

__theorem__: Colloquially,

**the**sum

**of**

**a**sequence

**of**cardinals

**is**strictly less than

**the**product

**of**

**a**sequence

**of**larger cardinals

**.**

__**__If S

**is**

**a**set

**of**sentences

**of**first-order logic and B

**is**

**a**consistent

**subset**

**of**S, then B

**is**included in

**a**set

**that**

**is**maximal among consistent subsets

**of**S

**.**

**The**special case where S

**is**

**the**set

**of**all first-order sentences in

**a**given signature

**is**weaker, equivalent to

**the**Boolean prime ideal

__theorem__; see

**the**section " Weaker forms " below

**.**

__**__

**The**Baire category

__theorem__about complete metric spaces, and its consequences, such as

**the**open mapping

__theorem__and

**the**closed graph

__theorem__

**.**

__**__Gödel's completeness

__theorem__for first-order logic: every consistent set

**of**first-order sentences has

**a**completion

**.**

__**__

**The**

**numbers**and are

**not**algebraic

**numbers**( see

**the**Lindemann – Weierstrass

__theorem__); hence they are transcendental

**.**

__**__More generally, Rademacher's

__theorem__extends

**the**differentiability result to Lipschitz mappings between Euclidean spaces:

**a**Lipschitz map ƒ: U → R < sup > m </ sup >, where U

**is**an open set in R < sup > n </ sup >,

**is**almost everywhere differentiable

**.**

__**__Artin reciprocity law,

**a**general

__theorem__in number theory

**that**provided

**a**partial solution to Hilbert's ninth problem

** and on

__**__Eunectes murinus,

**the**green anaconda,

**the**largest species,

**is**found east

**of**

**the**Andes in Colombia, Venezuela,

**the**Guianas, Ecuador, Peru, Bolivia, Brazil and

__on__

**the**island

**of**Trinidad

**.**

__**__See also Salmond

__on__" Citizenship and Allegiance ," in

**the**Law Quarterly Review ( July 1901, January 1902 ).

__**__This

**is**,

__on__

**the**whole, an informed and good account

**of**

**the**life and accomplishments

**of**one

**of**

**the**greatest influences

__on__

**the**development

**of**thought both Eastern and Western

**.**

__**__This

**is**

**a**distinguished work

**which**stands out from, and above, many

**of**

**the**books and articles

**which**have ben written in this century

__on__Avicenna ( Ibn Sīnā ) ( A

**.**D

**.**980 – 1037 ).

__**__Minimum level required for POWER4 hardware and

**the**last release

**that**worked

__on__

**the**Micro Channel architecture

0.131 seconds.