# What is the outer measure of Vitali set? [duplicate]

Possible Duplicate:
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?

## marked as duplicate by t.b., Asaf Karagila♦, Martin Sleziak, Jonas Teuwen, Jack SchmidtAug 15 '12 at 16:10

• It isn't determined from the usual description alone. – t.b. Aug 15 '12 at 15:41
• @t.b. Many thanks, I guess this is a duplicate then. I will flag it. – Vital Aug 15 '12 at 15:43
• No need to flag it. See also: math.stackexchange.com/questions/157532, math.stackexchange.com/q/32214 – t.b. Aug 15 '12 at 15:43
• @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. – Vital Aug 15 '12 at 15:47

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