  We study analysis on the cone of discrete Radon measures over a locally
compact Polish space $X$. We discuss probability measures on the cone and the
corresponding correlation measures and correlation functions on the sub-cone of
finite discrete Radon measures over $X$. For this, we consider on the cone an
analogue of the harmonic analysis on the configuration space developed in [12].
We also study elements of the difference calculus on the cone: we introduce
discrete birth-and-death gradients and study the corresponding Dirichlet forms;
finally, we discuss a system of polynomial functions on the cone which satisfy
the binomial identity.
