Proposition 3.83 . [02N7]

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Proposition 3.83.

Let $\Lambda$ be a convex polyhedron in $N_{\mathbb{R}}$ and $f_{1},\dots,f_{l}$ functions in ${\mathscr{D}}(\Lambda)$ (respectively, in ${\overline{\mathscr{D}}}(\Lambda)$ ). Then the functions

(1)

$\sum_{i}\lambda_{i}f_{i}$ for any $\lambda_{i}\in\mathbb{R}$ ,
(2)

$\max_{i}\{f_{i}\}$ , $\min_{i}\{f_{i}\}$

are also in ${\mathscr{D}}(\Lambda)$ (respectively, in ${\overline{\mathscr{D}}}(\Lambda)$ ).