= Affine upper envelope
{title2=$\overline f(x)=\inf\{a(x):a\in A(K),\ a\ge f\}$}
For a bounded real <function> on a compact convex set, this envelope is the infimum of its continuous affine majorants. It is finite, concave and <upper semicontinuous>, and dominates the <function>. For continuous <functions> it describes the maximal integral among <probability measures> with a specified <barycenter>. Its homogeneity, subadditivity and affine-translation identities give the <supporting measure lemma for affine upper envelopes>.
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