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When does an inner product on $C(K)$ come from integration?

Let $K$ be a compact Hausdorff space and suppose $\langle \cdot, \cdot \rangle$ is an inner product on $C(K)$ such that $\langle f, g \rangle \ge 0$ whenever $f(t),g(t)\ge 0$ for all $t \in K$. It fol …
Mark Roelands's user avatar