# Boole inequality

Let $(\Omega,\mathcal{F},P)$ be a probability space and $\{A_{1},A_{2},\cdots\}$ be a sequence of events such that $\{A_{1},A_{2},\cdots\}\subset\mathcal{F}$. Then

 $P(\bigcup_{n=1}^{\infty}A_{n})\leq\sum_{n=1}^{\infty}P(A_{n}).$
Title Boole inequality BooleInequality 2013-03-22 15:45:07 2013-03-22 15:45:07 georgiosl (7242) georgiosl (7242) 4 georgiosl (7242) Theorem msc 60A99