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A note on the σ-compactness of sets of probability measures on metric spaces

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  • Luque-Vásquez, Fernando
  • Adolfo Minjárez-Sosa, J.

Abstract

In this note we prove the σ-compactness of a set of probability measures with finite expectation, defined on metric spaces. Our result is motivated by the problem of the existence of measurable selectors for multifunctions in decision problems where the action space is a set of probability measures.

Suggested Citation

  • Luque-Vásquez, Fernando & Adolfo Minjárez-Sosa, J., 2014. "A note on the σ-compactness of sets of probability measures on metric spaces," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 212-214.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:212-214
    DOI: 10.1016/j.spl.2013.10.015
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    References listed on IDEAS

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    1. C. J. Himmelberg & T. Parthasarathy & F. S. VanVleck, 1976. "Optimal Plans for Dynamic Programming Problems," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 390-394, November.
    2. Anna Jaśkiewicz & Andrzej Nowak, 2011. "Stochastic Games with Unbounded Payoffs: Applications to Robust Control in Economics," Dynamic Games and Applications, Springer, vol. 1(2), pages 253-279, June.
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