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For a locally compact Hausdorff space $X$, $C_c(X)$ consists of continuous functions whose support is compact. A positive linear functional on this space, bounded on each fixed compact support, is represented by a Radon measure. For a locally compact group with Haar measure, these functions are dense in $L^p$ for $1\le p<\infty$.

A vector Radon measure has Radon measures as components. The vector form of the Riesz-Markov-Kakutani representation theorem identifies finite such measures with bounded functionals on $C_0(\Omega ;{\mathbb{R}}^n)$.