Closed selections of Vitali's type (Q2116069)

Given a Polish space endowed with an action of a group \(G\) and a \(G\)-invariant measure, the authors investigate measurability properties of closed \(H\)-selections for a subgroup \(H\) of \(G\), i.e., closed selections on each orbit of \(H\). The result extends in a more abstract setting the classical Vitali construction of a one point \(\mathbb{Q}\)-selection on \(\mathbb{R}\), which is always non-Lebesgue measurable.