Category:Dynkin Systems

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This category contains results about Dynkin Systems.
Definitions specific to this category can be found in Definitions/Dynkin Systems.

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 $\DD$, $\ds \bigcup_{n \mathop \in \N} D_n \in \DD$