# Why outer measure of Vitali set is greater than 0 or equals to 0?

In the following conservation (link below) https://www.researchgate.net/post/Bounds_on_the_outer_measure_of_Vitali_Set_in_0_1

There is a person who said that outer measure of the Vitali set on $$[0,1]$$ is greater than 0. Anyone can tells me why?

1. $$m^{\star}(A) \ge 0$$

2. $$m^{\star}(A) =0$$ implies $$A$$ is measurable.

Let $$\mathcal{V}$$ denote the Vitali set.

If $$m^{\star} (\mathcal{V}) \not >0$$ , then $$m^{\star}(\mathcal{V}) =0$$ implies $$\mathcal{V}$$ is measurable.

But $$\mathcal{V}$$ is non measurable.

Infact $$\mathcal{V}$$ has full outer measure.

( See here)