中文摘要：

研究了随机变量序列正则和函数的重对数律，作为应用，给出了正的随机变量序列部分和乘积的重对数律。同时，还获得了独立随机变量阵列相应的单对数律结果。

英文摘要：

The law of the iterated logarithm for the function of normalized sums of random variables is obtained. As its application, the law of the iterated logarithm for the products of sums of positive random variables is obtained. The corresponding law of single logarithm is also obtained for the array of independent and identically distributed random variables.