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Majorization on a Partially Ordered Set

F. K. Hwang
Proceedings of the American Mathematical Society
Vol. 76, No. 2 (Sep., 1979), pp. 199-203
DOI: 10.2307/2042988
Stable URL: http://www.jstor.org/stable/2042988
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Majorization on a Partially Ordered Set
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Abstract

We extend the classical concept of set majorization to the case where the set is partially ordered. We give a useful property which characterizes majorization on a partially ordered set. Quite unexpectedly, the proof of this property relies on a theorem of Shapley on convex games. We also give a theorem which is parallel to the Schur-Ostrowski theorem in comparing two sets of parameters in a function.

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