Lebesgue Outer Measure: Vitali Set

Question

What is the Lebesgue outer measure of a Vitali set and its complement over $\Omega=[0,1]$?

My first guess was zero and one but that was on my wrong idea that I can adjust the vitali set to lie within $[0,\varepsilon)$ changing it again and again... Also though its complement lies within $[\varepsilon,1]$ it is not guaranteed that there's a finer covering of it than that of $[\varepsilon,1]$.

score 1 · Accepted Answer · edited Apr 13 '17 at 12:20

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As is noted here:

What is the outer measure of Vitali set?

You may change the vitali set to have any possible Outer Measure if you construct it properly.

In general, it is not Lebesgue Measurable.

edited Apr 13 '17 at 12:20

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answered Sep 01 '14 at 20:32

Anthony Peter

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Ah so thats a duplicate - I'm sorry for that! – freishahiri Sep 01 '14 at 20:35
@Freeze_S No worries! – Anthony Peter Sep 01 '14 at 20:36

Lebesgue Outer Measure: Vitali Set

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