Definition:Dynkin System

Definition

Let $X$ be a set, and let $\DD \subseteq \powerset X$ be a collection of subsets of $X$.

Then $\DD$ is called a Dynkin system (on $X$) if and only if it satisfies the following conditions:

$(1): \quad X \in \DD$

$(2): \quad \forall D \in \DD: X \setminus D \in \DD$

$(3): \quad$ For all pairwise disjoint sequences $\sequence {D_n}_{n \mathop \in \N}$ in $\DD$, $\ds \bigcup_{n \mathop \in \N} D_n \in \DD$

Also see

• Results about Dynkin systems can be found here.

Source of Name

This entry was named for Eugene Borisovich Dynkin.

Sources

• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $5.1$
• 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $1.6$: Dynkin Classes