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Orderings and dilations of measures

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1757)

Abstract

If X is a compact convex subset of a locally convex space E, and if μ, λ are nonnegative measures on X, we have defined μ ≻ λ to mean that μ(f) ≧ λ(f) for each continuous convex function f on X. For finite dimensional spaces E, this ordering has long been of interest in statistics; it is used to defined “comparison of experiments.” A characterization in terms of dilations (defined below) has been given by Hardy, Littlewood, and Polya for one dimensional spaces, and by Blackwell [10], C. Stein, and S. Sherman for finite dimensional spaces. The general case has been proved by P. Cartier [15], based in part on the work of Fell and Meyer; this is the proof we present below. An entirely different approach has been carried out by Strassen [75].

Keywords

  • Borel Measur
  • Natural Projection
  • Convex Space
  • Closed Convex Cone
  • Compact Convex Subset

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). Orderings and dilations of measures. In: Phelps, R.R. (eds) Lectures on Choquet’s Theorem. Lecture Notes in Mathematics, vol 1757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48719-0_15

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  • DOI: https://doi.org/10.1007/3-540-48719-0_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41834-4

  • Online ISBN: 978-3-540-48719-7

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