Let $(X,\mathcal B,\mu)$ be a probability space, and let $\alpha$ and $\beta$ be finite $\mathcal B$-measurable partitions of $X$. For each atom $B \in \beta$ with $\mu(B)>0$ and each atom $A \in \alpha$, define the [conditional probability](/page/Conditional%20Probability) of $A$ relative to $B$ by
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\begin{align*}
\mu(A \mid B) := \frac{\mu(A \cap B)}{\mu(B)}.
\end{align*}
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Let $N_\beta := \bigcup\{B \in \beta : \mu(B)=0\}$. Define the conditional information function
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\begin{align*}
I_\mu(\alpha \mid \beta): X \to [0,\infty]
\end{align*}
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by setting, for $x \in A \cap B$ with $A \in \alpha$, $B \in \beta$, and $\mu(B)>0$,