关于经典强大数定律的一点注记

A note on the classic strong law of large numbers

有关概率论的教科书给出了sum from n=1 to∞(E|X_n|~p/a_n^p)＜∞条件下的经典强大数定律,且要求r.v.绝对矩的阶数p在(0,2)之间,但对于绝对矩阶数p＞2的情形,不能得到相应的结论．研究了矩的阶数p＞2的情形,得到了sum from n=1 to∞(E|X|^(2r)/a_n^(r+1))＜∞,且r＞1条件下独立r.v.序列的一类强大数定律．

The textbooks on probability theory, stipulate some classic strong laws of large numbers on the condition of ∞∑n=1 E｜Xn｜^p/a^p n〈∞ and require the order p of the absolute moment of random variable set between （0,2] , but they cant give corresponding results in the case when the order p of the absolute moment is larger than 2. This text studies the case when the order p is larger than 2, and gives a kind of strong laws of large numbers for a dependent random variable＇s sequence on the condition that they are related to ∞∑n=1 E｜X｜^2r/a^r＋1 n〈∞ and that r is larger than 1.