Definition:Join of Finite Sub-Sigma-Algebras

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

Let $\AA, \BB \subseteq \Sigma$ be finite sub-$\sigma$-algebras.

The join of $\AA$ and $\BB$ is the finite sub-$\sigma$-algebra defined as:
 * $\ds \AA \vee \BB := \map \sigma {\AA \cup \BB}$

where $\map \sigma \cdot$ denotes the generated $\sigma$-algebra.