= Compact-metric representation by Cantor-space pullback
Given a continuous surjection $h:\Omega\to K$ from <Cantor space> to a nonempty <compact metric space>, the pullback $f\mapsto f\circ h$ is a unital <isometric embedding> of $C(K)$ into $C(\Omega)$. Transport a normalized <positive linear functional> to its image, take a <positive extension from a unital subspace of C(K)>, and represent that extension on Cantor space. The <pushforward measure> $h_*P$ then represents the original functional.
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