  In this paper, we study random sampling on reproducing kernel space $V$,
which is a range of an idempotent integral operator. Under certain decay
condition on the integral kernel, we show that any element in $V$ can be
approximated by an element in a finite-dimensional subspace of $V$. Moreover,
we prove with overwhelming probability that random points uniformly distributed
over a cube $C$ is stable sample for the set of functions concentrated on $C$
