19.7.15 The Okounkov bodies of almost semigroupsA31E0D5C79D3

Fix an integer $n\geq 0$. Fix a closed convex cone $C\subseteq \mathbb {R}^{n}\times \mathbb {R}_{\geq 0}$ such that $C\cap \{ x_{n+1}=0\} =\{ 0\} $. Here $x_{n+1}$ is the last coordinate of $\mathbb {R}^{n+1}$.