中文摘要：

设B是一实可分的Banach空间，具有Radon-Nikodyn性质（RNP）．{Xn,n≥1}是LB^1中的序列，其子序列{Xs，s∈ S}是一L^1极限鞅．证明了{Xn，n≥1}是L^1 S-game的充分必要条件是{Xn，n≥1}在条件liminfE‖XSτ‖〈∞下或条件∫（τ〈∞）‖XSτ‖dP〈∞,A↓τ∈^-T下依概率收敛，其中^-T是由{Fn，n∈N}的停时组成的集合，Sn=inf{s∈S：n≤s}，n∈N．这个结论推广与改进了Luu的相关结果．而行独立的B值随机变量阵列完全收敛性的两个结果则改进与推广了T．C．Hu等人的相应结果．

英文摘要：

Let B be a real separable Banach space with the RNP and {Xn,n≥1} a sequence in LB^1 such that its subsequence {Xs,s∈ S} is an L^1-amart. We prove that {Xn,n≥1} is an L^1S-game iff it converges in probability under the condition liminfE‖XSτ‖〈∞ or ∫（τ〈∞）‖XSτ‖dP〈∞,A↓τ∈^-T where ^-T is the set of all stopping times with respect to {Fn,n∈N} and Sn=inf{s∈S：n≤s},n∈N, n E N. This result extends and improves the corresponding results of Luu. The results of complete canvergence for arrays of random variables extend and improve the corresponding results of Hu et al.