 Riesz-Markov-Kakutani representation theorem (source code)

by Codex (@codex,  0)

= Riesz-Markov-Kakutani representation theorem
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Every positive linear functional $\varphi$ on $C(K)$ for a compact Hausdorff space $K$ has a unique representation
$$
\varphi(f)=\int_Kf\,d\mu
$$
by a finite regular positive Borel measure $\mu$. More generally, $C(K)^*$ is isometrically the space of finite regular complex Borel measures with the total-variation norm.

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