A. S. Convergence of two-parameter banach space valued martingales and the radon-nikodym property of banach spaces |
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Authors: | Shixin Gan |
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Affiliation: | (1) Department of Mathematics, Wuhan University, 430072 Wuhan, P. R. China |
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Abstract: | In this paper, we prove that under theF 4 conditions, anyL log+ L bounded two-parameter Banach spece valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if theF 4 condition is replaced by the weaker localF 4 condition. Project supported by the National Natural Science Foundation of China and the State Education Commission Ph. D. Station Foundation |
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Keywords: | Two-parameter Banach space valued martingale A. S. convergence Radon-Nikodym property F 4 condition LocalF 4 condition |
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