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April, 1981 Ordering of Distributions and Rearrangement of Functions
Ludger Ruschendorf
Ann. Probab. 9(2): 276-283 (April, 1981). DOI: 10.1214/aop/1176994468


Some characterizations of semiorders defined on the set of all probability measures on $R^n$ by the set of Schur-convex functions and by some subsets of all convex functions are proved. A connection of these results to the theorem of Hardy, Littlewood and Polya on the rearrangement of functions is discussed. Furthermore, by means of the results on the ordering of probability measures a generalization of a theorem on doubly stochastic linear operators due to Ryff is proved.


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Ludger Ruschendorf. "Ordering of Distributions and Rearrangement of Functions." Ann. Probab. 9 (2) 276 - 283, April, 1981.


Published: April, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0461.60026
MathSciNet: MR606989
Digital Object Identifier: 10.1214/aop/1176994468

Primary: 60B99
Secondary: 62H99

Keywords: Convex functions , diffusion , rearrangement , Stochastic semiorder

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 2 • April, 1981
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