Abstract
Using the basic separation theorem and the Riesz representation theorem we give a simple proof that any admissible rule for compact and certain non-compact parameter spaces is a Bayes rule. The result is employed to show that under suitable conditions any admissible rule is a Bayes rule against some proper prior where π i are proper priors of δ i We will also apply these theorems in both the parametric and non-parametric settings.
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