论文标题
事件的独立性弱和borel-cantelli引理的相反
Weak independence of events and the converse of the Borel--Cantelli Lemma
论文作者
论文摘要
Borel-cantelli引理的相反指出，如果$ \ {a_i \} _ {i = 1}^\ infty $是一系列独立事件，这样$ \ sum p（a_i）= \ infty $，那么几乎肯定会无疑会发生许多这些事件。 Erd \ h Os和Rényi证明，削弱独立性对成对独立性的状况就足够了。在本文中，我们研究了弱独立性的各种条件，这暗示了Borel-cantelli引理的相反的结论。我们将确定这些条件之间的确切含义关系。
The converse of the Borel-Cantelli Lemma states that if $\{A_i\}_{i=1}^\infty$ is a sequence of independent events such that $\sum P(A_i)=\infty$, then almost surely infinitely many of these events will occur. Erd\H os and Rényi proved that it is sufficient to weaken the condition of independence to pairwise independence. In this paper we study various conditions of weak independence that imply the conclusion of the converse of the Borel--Cantelli Lemma. We will determine the exact implicational relationship among these conditions.
