$p$-system

Definition

A $p$-system or product-system is the name given to a system of subsets of $X$, $P\subseteq\mathcal{P}(X)$ where it is closed under finite intersections, that is to say:

• Given $A,B\in P$ that $A\cap B\in P$

See also

• $d$-system (Dynkin system)
• A collection of subsets of $X$, $\mathcal{A}$ is a $\sigma$-algebra if and only if it is both a $p$-system and a $d$-system