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: XDX \in \mathcal D; A,BDA, B \in \mathcal D, ABA \subseteq B \Rightarrow BADB \setminus A \in \mathcal D; and AnAA_n \uparrow A, AnDA_n \in \mathcal D \Rightarrow ADA \in \mathcal D.

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