(i) | $\mathcal{G} \subseteq \mathcal{F}$ is a D470: Subsigma-algebra of $\mathcal{F}$ on $\Omega$ |

(ii) | $E \in \mathcal{F}$ is an D1716: Event in $P$ |

**conditional probability**of $E$ in $P$

*given*$\mathcal{G}$ is the D3161: Random real number \begin{equation} \mathbb{P}(E \mid \mathcal{G}) := \mathbb{E}(I_E \mid \mathcal{G}) \end{equation}