Abstract
A simple proof of the almost sure discreteness of a class of random measures which includes completely random measures is presented. The method of proof shows how one may extend the specific argument of Berk and Savage (Berk and Savage Contributions to Statistics, Jaroslev Hajek Memorial Volume, Reidel, Dordrecht, Boston, Massachusetts, London, 25 (1979)) and Lo and Weng (Ann. Inst. Statist. Math. 41 (1989) 227), for the Dirichlet and weighted gamma processes, respectively. The technique is based on a disintegration argument which reveals the role of a necessary positivity condition.
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