Nonnegative idempotent kernels (Q1115982)

From authors' introduction: ``The structure of nonnegative idempotent kernels is presented in this paper. The results here generalize (and are based on) earlier results and ideas of Blackwell. Topologized versions of our results along with applications are also given....Nonnegative idempotent kernels are natural generalizations of infinite dimensional nonnegative idempotent matrices, whose structures are already known. The simplest of such kernels are of the form \(Q(x,E)=f(x)L(E),\) where f is a strictly positive Borel measurable function, L is a nonnegative Borel measure, and \(\int f dL=1.\) For example, when X is the set of reals \(\geq 1\) and m is the Lebesgue measure, then \((1/x^ 2)\cdot m(E)\) defines such a kernel. As we will show in this paper, general nonnegative idempotent kernels are, in most cases, obtained by piecing together kernels of the above type.''