The problem on the measure of the union of line segments in the plane with restrictions on the set of their ends
The paper consider the following question: let \(\varphi\) be bijection between two zero measure sets \(A\) and \(B\) of the unit interval. If \(S(A, B, \varphi)\) denotes the union of all segment in the plane with endpoints \((a, 0)\) and \((\varphi(a), 1)\), for some \(a \in A\), what about the measure of \(S(A, B, \varphi)\)? The paper is written in Russian, thus it is not accessible to everyone.
scientific article; zbMATH DE number 7440283