A Dynkin system contains , is closed under complements, and is closed under countable disjoint unions. Equivalently, it contains differences whenever are members.
Every Dynkin system containing a pi-system also contains the sigma-algebra . Equivalently, the Dynkin system generated by a pi-system equals the sigma-algebra it generates.
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A Dynkin system (also known as a π-system or a Dynkin π-system) is a collection of sets that satisfies certain properties, making it useful in measure theory and probability. Specifically, a collection \( \mathcal{D} \) of subsets of a given set \( X \) is called a Dynkin system if it satisfies the following properties: 1. **Contains the entire set**: \( X \in \mathcal{D} \).