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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Continuous functions on the space of probabilities


Authors: S. C. Bagchi and B. V. Rao
Journal: Proc. Amer. Math. Soc. 95 (1985), 474-475
MSC: Primary 60B99; Secondary 28A33
DOI: https://doi.org/10.1090/S0002-9939-1985-0806090-8
MathSciNet review: 806090
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Abstract | References | Similar Articles | Additional Information

Abstract: Weiss and Dubins discovered that any continuous function $ g(P)$ on the space of probabilities $ \mathcal{P}$ of a compact Hausdorff space $ K$ is of the form $ \smallint f\;d{P^\infty }$ for some continuous function $ f$ on $ {K^\infty }$. A short proof is given here.


References [Enhancements On Off] (What's this?)

  • [1] Lester E. Dubins, Bernstein-like polynomial approximation in higher dimensions, Pacific J. Math. 109 (1983), no. 2, 305–311. MR 721922
  • [2] Kôsaku Yosida, Functional analysis, 4th ed., Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 123. MR 0350358

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0806090-8
Keywords: Weak* convergence of probabilities, closed range theorem
Article copyright: © Copyright 1985 American Mathematical Society