Abstract
It is shown here that for any Banach spaceE-valued amart (X n) of classB, almost sure convergence off(Xn) tof(X) for eachf in a total subset ofE * implies scalar convergence toX.
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Marraffa, V. On almost sure convergence of amarts and martingales without the Radon-Nikodym property. J Theor Probab 1, 255–261 (1988). https://doi.org/10.1007/BF01246628
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DOI: https://doi.org/10.1007/BF01246628