ThmDex – An index of mathematical definitions, results, and conjectures.
F8140
Formulation 0
Let $x_1, \dots, x_N \in \mathbb{R}$ each be a D993: Real number.
Let $\lambda_1, \dots, \lambda_N \in [0, \infty)$ each be an D4767: Unsigned real number such that
(i) \begin{equation} \sum_{n = 1}^N \lambda_n = 1 \end{equation}
Then \begin{equation} \min(x_1, \dots, x_N) \leq \sum_{n = 1}^N \lambda_n x_n \leq \max(x_1, \dots, x_N) \end{equation}