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An extension of Prohorov's theorem for transition probabilities with applications to infinite-dimensional lower closure problems

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Abstract

A criterion for the relative weak compactness of sets of transition probabilitieson T×B(S) was given by Balder (1984 a),T being a space equipped with a fixed measure andB(S) denoting the σ-algebra of a standard Borel spaceS. This result, which generalizes Prohorov's classical tightness criterion, is extended here so as to cover the case where the spaceS is σ-standard Borel. As a consequence, the method applied in Balder (1984 a) now yields a new general infinite, dimensional lower closure result that can be used in the existence theory for optimal control.

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  1. Mathematical Institute, University of Utrecht, Utrecht (Olanda)

    E. J. Balder

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  1. E. J. Balder
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Balder, E.J. An extension of Prohorov's theorem for transition probabilities with applications to infinite-dimensional lower closure problems. Rend. Circ. Mat. Palermo 34, 427–447 (1985). https://doi.org/10.1007/BF02844536

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