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Mathematics · Glossary

What is pi-system?

Also known as: lambda-system

Definition 9.3 University Mathematics — Year 3 · Chapter 9 — Measure Theory

A π\pi-system is a family stable under finite intersections. A λ\lambda-system (Dynkin class) is a family D\mathcal D with: X∈DX \in \mathcal D; A,B∈DA, B \in \mathcal D, A⊆BA \subseteq B ⇒\Rightarrow B∖A∈DB \setminus A \in \mathcal D; and An↑AA_n \uparrow A, An∈DA_n \in \mathcal D ⇒\Rightarrow A∈DA \in \mathcal D.

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