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Transactions of the American Mathematical Society

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

 
 

 

The order convergence of martingales indexed by directed sets


Author: Kenneth A. Astbury
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0610961-6
Article copyright: © Copyright 1981 American Mathematical Society

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