A note on standard borel and related spaces

Abstract

The following is a fundamental construction in the theory of point processes: For a measurable space (X, ɛ) let X◃ denote the set of all measures on (X, ɛ) taking only values in the set ℕ (and so each p ∈ X◃ is a finite measure, since p(X) ∈ ℕ); put ɛ◃ = σ(ɛ◊), where ɛ◊ is the set of all subsets of X◃ having the form {p ∈ X◃: p(E) = k} with E ∈ ɛ and k ∈ ℕ.