Let $V$ be a real [vector space](/page/Vector%20Space) over $\mathbb{R}$, let $C \subset V$ be a subset such that for every $u,v \in C$ and every $t \in [0,1]$ the point $(1-t)u + tv$ belongs to $C$, and let $f: C \to \mathbb{R}$ be a function such that for every $u,v \in C$ and every $t \in [0,1]$,
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\begin{align*}
f((1-t)u + tv) \le (1-t)f(u) + t f(v).
\end{align*}
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For every integer $m \ge 1$, every finite family of points $x_1,\ldots,x_m \in C$, and every finite family of coefficients $\lambda_1,\ldots,\lambda_m \in [0,\infty)$ satisfying