# [ilmath]p[/ilmath]-system

## Definition

A [ilmath]p[/ilmath]-system or product-system[1][Note 1] is the name given to a system of subsets of [ilmath]X[/ilmath], [ilmath]P\subseteq\mathcal{P}(X)[/ilmath] where it is closed under finite intersections[1], that is to say:

• Given [ilmath]A,B\in P[/ilmath] that [ilmath]A\cap B\in P[/ilmath]