Some limit properties of the multivariate function sequences of the nonnegative integer-valued random variables are studied by usi ng the differentiation of measures on a net and the conditional moment generating functions,and some strong limit theorems related to the co nditional expectations are obtained.%利用测度关于网的微分法和条件矩母函数的工具研究非负整值随机变量多 元函数序列的极限性质，得到了若干与条件数学期望有关的强极限定理．
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