Space of continuous compactly supported functions
= Space of continuous compactly supported functions
{title2=$C_c(X)$}
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 $1\leq p<\infty$.