两指标B值鞅的A.S.收敛性与B空间的Radon-Nikodym性

A.S. Convergence of Two-Parameter Banach Space Valued Martingales and the Radon-Nikodym Property of Banach Space

本文证明了在F4条件下，任一Llog+L有界的两指标B值鞅几乎处处收敛到一可积的B值随机变量当且仅当B空间有Radon-Nikodym性质．进一步还证明了在更弱的局部F4条件下，上述结论也成立．

In this paper, we prove that under the F4 condition, any Llog+ L bounded two-parameter Banach Space 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 the F4 condition is replaced by the weaker local F4 condition.