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Entropy of a finite measurable partition

{title2=$H_\mu(\xi\mid\eta)$}

For finite partitions $\xi,\eta$,
$$
H_\mu(\xi\mid\eta)
=\sum_{B\in\eta}\mu(B)H_\mu(\xi\mid B)
=H_\mu(\xi\vee\eta)-H_\mu(\eta).
$$
<Conditioning reduces entropy>, so $H_\mu(\xi\mid\eta)\leq H_\mu(\xi)$.

Conditional entropy of finite measurable partitions

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 108 / 3 / Solution

Conditional entropy of finite measurable partitions ( $H_{μ} (ξ ∣ η)$ )

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Conditional entropy of finite measurable partitions (Hμ​(ξ∣η))

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