中文摘要：

设{Xn；n≥1}为均值为零、方差有限的B值m相依随机变量列．利用B值m相依随机变量列弱收敛定理讨论了{Xn；n≥1}的完全收敛性及重对数律的精确渐进性．若记Sn=n∑（j=1）Xj，1≤P〈2，得到了P{｜｜Sn｜｜≥εn^1/p}的一类加权级数在ε→0时的极限以及，P{｜｜Sn｜｜≥ε√nlog n}的一类加权级数在ε→0时的极限．所得结果是实值i．i．d．随机变量序列完全收敛性及重对数律的精确渐进性质的进一步推广．

英文摘要：

Let {Xn;n≥1} zeros and finite variances, random variables, we studi a sequence of m-dependent Banach space valued random variables with mean y using the weak convergence theorem of m-dependent Banach space valued the precise asymptotics of the complete convergence and the law of the iterated logarithm for the sequence {Xn;n≥1}.Set Sn=n∑（j=1）Xj,1≤P〈2,we have the limits of a weighed infinite series of P{｜｜Sn｜｜≥εn^1/p} as ε→0 and the limits of a kind of weighed infinite series of P{｜｜Sn｜｜≥ε√nlog n} as ε→0 We extended the results of the precise asymptotics of the complete convergence and the law of the iterated logarithm for real valued i. i. d. random variables.