PlanetMath: Vitali's Theorem

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Vitali's Theorem

(Theorem)

There exists a set $V\subset [0,1]$ which is not Lebesgue measurable. Notice that this result requires the Axiom of Choice.

"Vitali's Theorem" is owned by paolini.

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Other names:

existence of non measurable sets

Attachments:: proof of Vitali's Theorem (Proof) by paolini
example of function not Lebesgue Measurable with measurable level sets (Example) by cvalente

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Cross-references: axiom of choice, Lebesgue measurable
There are 3 references to this entry.

This is version 2 of Vitali's Theorem, born on 2003-07-17, modified 2004-03-31.
Object id is 4466, canonical name is VitalisTheorem.
Accessed 7378 times total.

Classification:

28Axx (Classical measure theory)

Pending Errata and Addenda

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