Space of continuous compactly supported functions ($C_c(X)$)

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 $1\le p<\infty$.