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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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The order convergence of martingales indexed by directed sets
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by Kenneth A. Astbury PDF
Trans. Amer. Math. Soc. 265 (1981), 495-510 Request permission

Abstract:

We obtain a condition on the underlying family of $\sigma$-algebras which is properly weaker than the Vitali property but which is also a sufficient condition for the order convergence of martingales of semibounded variation. We also obtain a sufficient condition for the order convergence of martingales of semibounded variation in terms of the finiteness of the extreme order limits of martingales of bounded variation.
References
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 265 (1981), 495-510
  • MSC: Primary 60G42; Secondary 60F15, 60G44
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0610961-6
  • MathSciNet review: 610961