关于削弱辛钦大数定律成立条件的一点探讨

The Study on Weakening the Tenable Conditions of Khinchine Law of Large Numbers

我们常见的一些大数定律,从车比雪夫大数定律、马尔可夫大数定律到辛钦大数定律都是判断一个随机变量服从大数定律的充分条件,且要求条件较强,这在应用中具有很大的局限性。本文尝试了对辛钦大数定律的条件加以削弱。

Some laws of large numbers that are often seen by us, such as Chebyhev Law of Large Numbers, Markov Law of Large Numbers and Khinchine Law of Large numbers, are all adequate conditions to judge that a random variable {ξn} is subordinated to the law of large numbers,, and they all demand the conditions much, which has great limitation in the application. The paper manages to weaken the conditions of Khinchine Law of Large Numbers.