Let $(X,\mathcal B,\mu)$ be a probability space, and let $\alpha=\{A_1,\dots,A_k\}$ be a finite measurable partition of $X$ such that $\mu(A_i)>0$ for every $i\in\{1,\dots,k\}$. Define the entropy of $\alpha$ by
\begin{align*}
0\le H_\mu(\alpha)\le \log k.
\end{align*}
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Moreover, $H_\mu(\alpha)=0$ if and only if one atom of $\alpha$ has measure $1$, and $H_\mu(\alpha)=\log k$ if and only if $\mu(A_i)=1/k$ for every $i\in\{1,\dots,k\}$.