Definition 11.1.8.label Let $\curl{A_\al }_{\al\in J}$ be a family of $\s$-algebras then $\caps{}{\al\in J}A_{\al}$ is a $\s$-algebra so given a family $\cali{E}$ of subsets of $X$ there exists a smallest $\s$-algebra $\cali{M}(\cali{E})$ containing $\cali{E}$ called the generating $\s$-algebra of $\cali{E}$