Es sei ${\displaystyle {}M}$ eine Menge und ${\displaystyle {}{\mathcal {E}}\subseteq {\mathcal {E}}'}$ seien Mengensysteme. Dabei sei ${\displaystyle {}{\mathcal {E}}'}$ in der von ${\displaystyle {}{\mathcal {E}}}$ erzeugten ${\displaystyle {}\sigma }$-Algebra ${\displaystyle {}\sigma ({\mathcal {E}})}$ enthalten. Zeige

${\displaystyle {}\sigma {\left({\mathcal {E}}\right)}=\sigma {\left({\mathcal {E}}'\right)}\,.}$