Boole's Inequality

From GM-RKB
(Redirected from union bound)
Jump to navigation Jump to search

A Boole's Inequality is an inequality relation that states the total probability of a finite or countable set union is no greater than the sum of the individual probabilities.



References

2016

Formally, for a countable set of events A1, A2, A3, ..., we have
[math]\displaystyle{ {\mathbb P}\biggl(\bigcup_{i} A_i\biggr) \le \sum_i {\mathbb P}(A_i). }[/math]
In measure-theoretic terms, Boole's inequality follows from the fact that a measure (and certainly any probability measure) is σ-sub-additive.