Definition:Join of Finite Partitions

Definition
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $\xi, \eta$ be finite partitions of $\Omega$.

The join of $\xi$ and $\eta$ is the finite partition defined as:
 * $\ds \xi\vee\eta := \set { A\cap B : A\in\xi, B\in\eta }$