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中文摘要：
本文在Banach空间B是p可光滑（1〈P≤2）的条件下获得了B值弱相依随机变量序列正则和极限点集的上界．作为应用，由B值y-混合随机变量序列的强大数定律刻划了Banach空间的p可光滑性，在不要求混合系数ψn和ψn趋于0而是在inf n≥1ψn=0或inf n≥1ψn=0条件下，获得了B值相依随机变量序列有关强大数定律的一些结果．
英文摘要：
In this paper, we obtain the almost sure bound of normal sum of B-valued weakly dependent random variables under the assumption that Banach space B is p-smoothable （1 〈： p 〈： 2）. As its application, we characterize p-smoothness of Banach space through the strong law of large numbers of B-valued y-mixing random variables, and obtain some results on the strong law of large numbers for B-valued dependent random variables without assumption on rate of tending to zero of ψ and ψ-mixing parameters ψn and ψn but under the assumption that inf n≥1ψn=0 or inf n≥1ψn=0 respectively.
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