Solution
= Solution
The <Shannon entropy> of a finite-valued <random variable> is
$$
\boxed{H(X)=-\sum_{x\in\mathcal A_X}P_X(x)\log_2P_X(x),\qquad0\log_2 0=0.}
$$
An <epsilon-sufficient set> is a subset $S\subseteq\mathcal A_X$ retaining all but at most $\epsilon$ of the probability:
$$
\boxed{\Pr(X\in S)=\sum_{x\in S}P_X(x)\geq1-\epsilon.}
$$
Usually $0\leq\epsilon\leq1$. Sufficiency here concerns retained probability mass, rather than a <sufficient statistic>.