Abstract
Random orders on \(\mathbb{N}\) invariant under permutations are called exchangeable. The compact and convex set of all random total orders is shown to be a Bauer simplex whose set of extreme points, the socalled totally ordered paintbox processes, is homeomorphically parametrized by “almost uniform” distributions on the unit interval, i.e. by probability measures w on [0, 1] whose distribution functions are w-almost surely the identity.
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Hirth, U., Ressel, P. Exchangeable Random Orders and Almost Uniform Distributions. Journal of Theoretical Probability 13, 609–634 (2000). https://doi.org/10.1023/A:1007805925957
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DOI: https://doi.org/10.1023/A:1007805925957