Sets with doubleton sections, good sets and ergodic theory

A. Klopotowski, M. G. Nadkarni, H. Sarbadhikari, S. M. Srivastava
2002 Fundamenta Mathematicae  
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. 2000 Mathematics Subject Classification: Primary 60A05, 47A35; Secondary 28D05, 37Axx.
doi:10.4064/fm173-2-3 fatcat:ssud7khqxfdybinpjqzgyajj4e