PomeDefinition 21.11.9.8F179BE28950 Let $f\colon N\rightarrow [-\infty ,\infty ]$. The lower convex envelope of $f$ is defined as
\[ \operatorname{CE}f\coloneqq \sup \{ F\in \mathrm{Conv}(N): F\leq f \} . \]
It follows from proposition 21.11.8 that $\operatorname{CE}f\in \mathrm{Conv}(N)$.
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