Let $(\Omega,\mathcal F,\mathbb P)$ be a probability space, let $X\in L^1(\Omega,\mathcal F,\mathbb P)$, and let $(A_i)_{i=1}^n$ be a finite information partition. Let $\mathcal G=\sigma(A_1,\dots,A_n)$. If $\mathbb P(A_i)>0$ for each $i$, then
\begin{align*}
\mathbb E[X\mid\mathcal G]
=\sum_{i=1}^n \left(\frac{1}{\mathbb P(A_i)}\int_{A_i} X\,d\mathbb P\right)\mathbb 1_{A_i}.
\end{align*}