Monotone Class

Overview

Definition

A family of sets {% M %} is a monotone class if given a sequence of sets {% A_i %} such that either

• {% A_n \subset A_{n+1} \; and \; \cup_{n=0}^\infty A_n = A %}
• {% A_{n+1} \subset A_n \; and \; \cap_{n=0}^\infty A_n = A %}

then {% A \in M %}

(see cohen pg 5)