ABSTRACT
We begin with a treatment of weak convergence on a general space S with a metric ρ, i.e., a function with (i) ρ(x,x) = 0, (ii) ρ(x, y) = ρ(y, x), and (iii) ρ(x, y) + ρ(y, z) ≥ ρ(x, z). Open balls are defined by {y : p(x, y) < r} with r > 0 and the Borel sets S are the σ-field generated by the open balls. Throughout this section we will suppose S is a metric space and S is the collection of Borel sets, even though several results are true in much greater generality. For later use, recall that S is said to be separable if there is a countable dense set, and complete if every Cauchy sequence converges.
