Exchangeable Random Measures in the Plane

Abstract

The main purpose of this paper is to derive de Finetti-type representations of arbitrary separately or jointly exchangeable random measures. By this is meant representations of the distributions of xi as unique mixtures (convex combinations) of so called extreme exchangeable distributions. The existence of such integral representations is essentially a consequence of general theory so the author's main point is to describe the extreme measures explicitly. Through suitable Borel isomorphisms from the two spaces, one may easily reduce the problem to the special case when X and Y are real intervals, equipped with corresponding restrictions lambda and mu of Lebesgue measure (henceforth always denoted by lambda). Keywords: Ergodic distributions, Random variables.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1988
Accession Number
ADA201055

Entities

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  • Olav Kallenberg

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  • University of North Carolina at Chapel Hill

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