Dynkin system

A Dynkin system, named after Eugene Dynkin, is a collection of subsets of another universal set ${\displaystyle \Omega }$ satisfying a set of axioms weaker than those of σ-algebra. Dynkin systems are sometimes referred to as λ-systems (Dynkin himself used this term) or d-system. These set families have applications in measure theory and probability.

A major application of λ-systems is the π-λ theorem, see below.

Let Ω be a nonempty set, and let ${\displaystyle D}$ be a collection of subsets of Ω (i.e., ${\displaystyle D}$ is a subset of the power set of Ω). Then ${\displaystyle D}$ is a Dynkin system if

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