有限概率空间中的独立事件组

The System of Independent Events in Finite Probability Space

设（Ω、F、P）为有限概率空间：|Ω|＝n，A＝｛Ai：1≤i≤k｝为一组事件，本文证明：i）当A为独立事件组时，k≤log2n；ii）当A为两两独立事件组时，k≤n—1，并且这些上界在一定的条件之下是可以达到的．

Let (Ω.F.P) be a finite probability space (|Ω|=n) and A={Ai: 1≤i≤k } be a system of events. In this paper we prove that: 1) If A is a system of independent events, then k≤log2n;2)If A is a system of events in which the events are independent one another, then k≤n-1, moreover, this upper bounds can be reached in certain conditions.