Lebesgue Outer Measure: Vitali Set

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 $[\varepsilon,1]$.