Lorentz and Gale–Ryser theorems on general measure spaces
Santiago Boza, Martin Křepela, Javier Soria · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2021
Based on the Gale–Ryser theorem [2, 6], for the existence of suitable $(0,1)$ -matrices for different partitions of a natural number, we revisit the classical result of Lorentz [4] regarding the characterization of a plane measurable set, in terms of its cross-sections, and extend it to general measure spaces.