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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Convergence of series of scalar- and vector-valued random variables and a subsequence principle in $L_ 2$
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by S. J. Dilworth PDF
Trans. Amer. Math. Soc. 301 (1987), 375-384 Request permission

Abstract:

Let $({d_n})_{n = 1}^\infty$ be a martingale difference sequence in ${L_0}(X)$, where $X$ is a uniformly convex Banach space. We investigate a necessary condition for convergence of the series $\sum {_{n = 1}^\infty {a_n}{d_n}}$. We also prove a related subsequence principle for the convergence of a series of square-integrable scalar random variables.
References
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 301 (1987), 375-384
  • MSC: Primary 60B12; Secondary 60G42
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0879579-X
  • MathSciNet review: 879579