monotone class

Monotone ClassFernando Sanz GÃÂ¡miz

A collection $\mathcal{M}$ of subsets of $\Omega$ is a monotone class if it is closed under increasing and decreasing sequences of sets, i.e.

1.

$A_{1}\subseteq A_{2}\subseteq A_{3},...\in\mathcal{M}\Rightarrow\bigcup A_{n}% \in\mathcal{M}$
2.

$A_{1}\supseteq A_{2}\supseteq A_{3},...\in\mathcal{M}\Rightarrow\bigcap A_{n}% \in\mathcal{M}$