Publication: Lorentz and Gale–Ryser theorems on general measure spaces
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2022-08-09
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https://www.cambridge.org/core/
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Abstract
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.
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[1] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988.
[2] D. Gale, A theorem on flows in networks, Pacific J. Math. 7 (1957), 1073–1082.
[3] M. Krause, A simple proof of the Gale-Ryser theorem, Amer. Math. Monthly 103 (1996), 335–337.
[4] G. G. Lorentz, A problem on plane measures, Amer. J. Math. 71 (1949), 417–426.
[5] J. V. Ryff, Measure preserving transformations and rearrangements, J. Math. Anal. Appl. 31 (1970), 449–458.
[6] H. J. Ryser, Combinatorial properties of matrices of zeros and ones, Can. J. Math. 9 (1957), 371–377.
[7] G. Sierksma and H. Hoogeveen, Seven criteria for integer sequences being graphic, J. Graph Theory 15 (1991), 223–231.
[8] W. Sierpi´nski, Sur les fonctions d’ensemble additives et continues, Fund. Math. 3 (1922), 240–246.