Sub-sigma-algebra ($\mathcal{G}\subseteq \mathcal{F}$)

A sigma-algebra $\mathcal{G}$ on the same underlying set as $\mathcal{F}$, with $\mathcal{G}\subseteq \mathcal{F}$. In probability theory it represents information retained from the original probability space and is a possible conditioning collection for a conditional expectation.