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Vitali-type set with given outer measure

Given that the construction of Vitali set is based on the axiom of choice. How can the outer measure of this set be calculated?

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    @t.b. If you post your comment as an answer with the references, I will accept it. This is what I was looking for. Thanks.2012-08-15

1 Answers 1

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On Vital's request:

There isn't just one Vitali set: each choice of representatives of the equivalence relation on $\mathbb{R}$ given by $x \sim y$ if and only if $y - x \in \mathbb{Q}$ yields what one calls a Vitali set. You can arrange them to have any given positive outer measure you want.

There are many threads on this site where Vitali sets were discussed, among which:

You can find a few more by Googling for "Vitali set" site:math.stackexchange.com