Sets with doubleton sections, good sets and ergodic theory
Volume 173 / 2002
Fundamenta Mathematicae 173 (2002), 133-158
MSC: Primary 60A05, 47A35; Secondary 28D05, 37Axx.
DOI: 10.4064/fm173-2-3
Abstract
A Borel subset of the unit square whose vertical and horizontal sections are two-point sets admits a natural group action. We exploit this to discuss some questions about Borel subsets of the unit square on which every function is a sum of functions of the coordinates. Connection with probability measures with prescribed marginals and some function algebra questions is discussed.
