A note on standard borel and related spaces

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. Dedicated to the 80th birthday of Klaus Krickeberg