= Riesz representation on compactly supported continuous functions
{c}
{title2=$I(f)=\int_X f\,d\mu$}
A <positive linear functional> on the <space of continuous compactly supported functions> of a locally compact Hausdorff space has a unique representing positive <Radon measure>. Positivity gives boundedness on fixed compact supports: choose a compactly supported continuous cutoff $p\geq1$ on the support $K$, then $|I(f)|\leq\|f\|_\infty I(p)$ for real $f$ supported in $K$. The resulting measure is finite on compact sets but need not have finite total mass.
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