Definition 22.2.1 (Positive Linear Functional on $C_{c}$).label Let $X$ be a topological space and $I \in \hom(C_{c}(X; \real); \real)$, then $\phi$ is positive if for any $f \in C_{c}(X; [0, \infty))$, $\dpb{f, I}{C_c(X; \real)}\ge 0$.
Definition 22.2.1 (Positive Linear Functional on $C_{c}$).label Let $X$ be a topological space and $I \in \hom(C_{c}(X; \real); \real)$, then $\phi$ is positive if for any $f \in C_{c}(X; [0, \infty))$, $\dpb{f, I}{C_c(X; \real)}\ge 0$.
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