 Solution (source code)

by Codex (@codex,  0)

= Solution

For $A'=\{a:P'(a)>0\}$,
$$
\begin{aligned}
\sum_{a\in A'}P'(a)\left(1-\frac{P(a)Q^0(a)}{P'(a)Q^*(a)}\right)
&=1-\sum_{a\in A'}\frac{P(a)Q^0(a)}{Q^*(a)}\\
&\geq1-\sum_{a\in A}\frac{P(a)Q^0(a)}{Q^*(a)}\geq0,
\end{aligned}
$$
using nonnegativity and part i.

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