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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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An extension of Skorohod’s almost sure representation theorem
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by David Blackwell and Lester E. Dubins PDF
Proc. Amer. Math. Soc. 89 (1983), 691-692 Request permission

Abstract:

Skorohod discovered that if a sequence ${Q_n}$ of countably additive probabilities on a Polish space converges in the weak star topology, then, on a standard probability space, there are ${Q_n}$-distributed ${f_n}$ which converge almost surely. This note strengthens Skorohod’s result by associating, with each probability $Q$ on a Polish space, a random variable ${f_Q}$ on a fixed standard probability space so that for each $Q$, (a) ${f_Q}$ has distribution $Q$ and (b) with probability 1, ${f_P}$ is continuous at $P = Q$.
References
  • A. V. Skorohod, Limit theorems for stochastic processes, Teor. Veroyatnost. i Primenen. 1 (1956), 289–319 (Russian, with English summary). MR 0084897
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 691-692
  • MSC: Primary 60B10
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0718998-0
  • MathSciNet review: 718998