Abstract

The background for this paper is a dynamic programming model with a Borel state space and compact action sets. A new simple proof of the compactness of a space of measures corresponding to randomized stationary policies is given, in a topology induced by Carathéodory functions on the state-action space. For this purpose an extension theorem for Carathéodory functions is proved, which is a new version of the Tietze's extension theorem for continuous functions.

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