The following is a fundamental construction in the theory of point processes: For a measurable space $(X,\mathcal{E})$ let  $\pp{X}{}$ denote the set of all measures on $(X,\mathcal{E})$ taking only values in the set $\Nat$ (and so each $p \in \pp{X}{}$  is a finite measure, since $p(X) \in \Nat$); put  $\pp{\mathcal{E}}{} = \sigma(\mathcal{E}_\Diamond)$, where  $\mathcal{E}_\Diamond$ is the set of all subsets of $\pp{X}{}$  having the form $\{ p \in \pp{X}{} : p(E) = k \}$ with $E \in  \mathcal{E}$ and $k \in \Nat$.