Definition:Dynkin System

Definition
Let $X$ be a set, and let $\mathcal D \subseteq \mathcal P \left({X}\right)$ be a collection of subsets of $X$.

Then $\mathcal D$ is called a Dynkin system (on $X$) it satisfies the following conditions:


 * $(1):\quad X \in \mathcal D$
 * $(2):\quad \forall D \in \mathcal D: X \setminus D \in \mathcal D$
 * $(3):\quad$ For all pairwise disjoint sequences $\left({D_n}\right)_{n \in \N}$ in $\mathcal D$, $\displaystyle \bigcup_{n \mathop \in \N} D_n \in \mathcal D$