Boole inequality

Let $(\mathrm{\Omega },ℱ,P)$ be a probability space and $\{A_1,A_2,\mathrm{\cdots }\}$ be a sequence of events such that $\{A_1,A_2,\mathrm{\cdots }\}\subset ℱ$. Then

$$P(\bigcup _{n=1}^{\mathrm{\infty }}{A}_n)\le \sum _{n=1}^{\mathrm{\infty }}P(A_n).$$

Title	Boole inequality
Canonical name	BooleInequality
Date of creation	2013-03-22 15:45:07
Last modified on	2013-03-22 15:45:07
Owner	georgiosl (7242)
Last modified by	georgiosl (7242)
Numerical id	4
Author	georgiosl (7242)
Entry type	Theorem
Classification	msc 60A99