 Let $p(Z)$ denote the observed data distribution, $M_0 = \big\{p^*_0(Z) = \operatorname*{arg\,max}_{q(Z)}   D_{KL}(p || q) \hspace{0.0cm} \text{ s.t. } \hspace{0.0cm}  \epsilon_l \leq g(q(Z)) \leq \epsilon_u, \ q(Z_0) = p(Z_0) \big\}$, and $M_0 = \big\{p^*_0(Z) = \operatorname*{arg\,max}_{q(Z)}   D_{KL}(p || q) \hspace{0.0cm} \text{ s.t. } \hspace{0.0cm} \epsilon_l \leq g(q(Z)) \leq \epsilon_u, \ q(Z_0) = p(Z_0) \big\}$. If $Z_0 \subseteq Z_0 \subseteq Z$, then $D_{KL}(p || p^*_0) \leq D_{KL}(p || p^*_0).$ 