Definition:Refinement of Partition (Probability Theory)

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

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

Then $\xi$ said to be a refinement of $\eta$ :
 * $\ds \forall A \in \eta : A = \bigcup \set {B \in \xi : B \subseteq A}$

It is written as:
 * $\eta \le \xi$