Boza, SantiagoKřepela, MartinSoria de Diego, Francisco Javier2024-03-042024-03-042022-01-0110.1017/prm.2021.37https://hdl.handle.net/20.500.14352/101901Based 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articleopen accessCross-sectionsNonincreasing rearrangementHardy-Littlewood-Póya relationAnálisis funcional y teoría de operadores1202 Análisis y Análisis Funcional