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