Existence of Vitali Set implies Subset of Unit Interval with Inner Measure Zero and Outer Measure 1

Theorem

Let us posit the existence of a Vitali set.

Then there exists a subset of the closed unit interval which has an inner measure of $0$ and an outer measure of $1$.

Proof

This theorem requires a proof. In particular: But first we need to know what an inner measure is. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1973: Thomas J. Jech: The Axiom of Choice ... (previous) ... (next): $1.$ Introduction: $1.4$ Problems: $4$