Convex support of an exponential family
= Convex support of an exponential family
{title2=$C=\overline{\operatorname{conv}(\operatorname{supp}\nu)}$}
The convex support is the closed <convex hull> of the canonical sufficient-statistic support. For a <minimal exponential family> it has nonempty interior. Means at finite interior natural parameters lie in that interior, because a supporting hyperplane at a boundary mean would force the sufficient statistic itself onto that hyperplane.