Definition:Sub-Sigma-Algebra

Definition
Let $X$ be a set, and let $\mathcal A, \mathcal B$ be $\sigma$-algebras on $X$.

Then $\mathcal B$ is said to be a sub-sigma-algebra or sub-$\sigma$-algebra of $\mathcal A$ iff $\mathcal B \subseteq \mathcal A$.