多指标随机阵列的0—1律

SOME ZERO-ONE LAWS FOR MULTI-DIMENSIONALLY INDEXED RANDOM ARRAYS

本文证明了多指标随机事件阵列的0—1律,多指标独立随机变量阵列的0—1律和多指标相互独立同分布随机变量阵列对称0—1律,这些结果均可看作是单指标随机序列的Borel—Cantelli引理,Kolmogorov无穷远0—Ⅰ律和Hewitt—Savage对称0—1律在多指标情形的推广。

In this paper, the author proves some zero-one laws for multidimensionally indexed random arrays, that is, the zero-one law for multidimensionally indexed arrays of random events and the zero-one law for multidimensionally indexed arrays of independent random variables and the zero-one law for multitimensionally indexed arrays of i. i. d. random variables. These results are regarded respectively as extensions of the Borel-Cantelli lemma and. the Kolmogorov zero-one law and the Hewitt-Savage zero-one law for One-dimensionally indexed random sequences.