Definition 19.2.9.78B565EC56CF We define $\overline{\mathcal{S}'(C)}_{>0}$ as the set of elements in the closure of $\mathcal{S}'(C)$ in $\hat{\mathcal{S}}(C)$ with positive volume. An element in $\overline{\mathcal{S}'(C)}_{>0}$ is called an almost semigroup in $C$.
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