Pi-system

In mathematics, a π-system (or pi-system) on a set ${\displaystyle \Omega }$ is a collection ${\displaystyle P}$ of certain subsets of ${\displaystyle \Omega ,}$ such that

• ${\displaystyle P}$ is non-empty.
• If ${\displaystyle A,B\in P}$ then ${\displaystyle A\cap B\in P.}$

That is, ${\displaystyle P}$ is a non-empty family of subsets of ${\displaystyle \Omega }$ that is closed under non-empty finite intersections.^{[nb 1]} The importance of π-systems arises from the fact that if two probability measures agree on a π-system, then they agree on the