monotone class
Monotone ClassFernando Sanz GÃÂ¡miz
Definition.
A collection^{} $\mathcal{M}$ of subsets of $\mathrm{\Omega}$ is a monotone class if it is closed under increasing and decreasing sequences of sets, i.e.

1.
${A}_{1}\subseteq {A}_{2}\subseteq {A}_{3},\mathrm{\dots}\in \mathcal{M}\Rightarrow \bigcup {A}_{n}\in \mathcal{M}$

2.
${A}_{1}\supseteq {A}_{2}\supseteq {A}_{3},\mathrm{\dots}\in \mathcal{M}\Rightarrow \bigcap {A}_{n}\in \mathcal{M}$
Title  monotone class 

Canonical name  MonotoneClass 
Date of creation  20130322 17:07:25 
Last modified on  20130322 17:07:25 
Owner  fernsanz (8869) 
Last modified by  fernsanz (8869) 
Numerical id  5 
Author  fernsanz (8869) 
Entry type  Definition 
Classification  msc 28A05 
Related topic  SigmaAlgebra 
Related topic  MonotoneClassTheorem 