Answer by orangeskid for Vitali-type set with given outer measure
Let $V$ be a $\mathbb{Q}$ vector subspace of $\mathbb{R}$ of codimension at most countable. Then $\mu^*(V\cap I) = \mu(I)$ for every $I$ interval.Proof:We may assumed wlog $1\in V$ (just divide by some...
View ArticleAnswer by JDH for Vitali-type set with given outer measure
One can proceed directly with the Vitali construction, without need for any scaling. Namely, just carry out the Vitali construction, but ensure that the resulting Vitali set is contained in the...
View ArticleClik here to view.
Answer by Jonas Meyer for Vitali-type set with given outer measure
This was my answer to the question as originally phrased: Once you have one nonmeasurable set with finite outer measure, you can get all positive values by rescaling. With the additional requirement...
View ArticleVitali-type set with given outer measure
Is it possible to construct a non-measurable set in $[0,1]$ of a given outer measure $x \in [0,1]$? This will probably require the axiom of choice. Does anyone have a suggestion?Edit: I forgot to...
View Article
