Proceedings of the Royal Society of Edinburgh: Section A Mathematics | 2021
Lorentz and Gale–Ryser theorems on general measure spaces
Abstract
Based on the Gale–Ryser theorem [2, 6], for the existence of suitable \n \n \n $(0,1)$\n \n -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.