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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Continuous functions on the space of probabilities
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by S. C. Bagchi and B. V. Rao PDF
Proc. Amer. Math. Soc. 95 (1985), 474-475 Request permission

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
  • Lester E. Dubins, Bernstein-like polynomial approximation in higher dimensions, Pacific J. Math. 109 (1983), no. 2, 305–311. MR 721922
  • Kôsaku Yosida, Functional analysis, 4th ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag, New York-Heidelberg, 1974. MR 0350358
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • 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