| Abstract
| - Let, for each t∈T, ψ( t, ۔) be a random measure on the Borel σ-algebra in ℝ d such that E ψ( t, ℝ d) k< ∞ for all k and let $\widehat{\psi}$( t, ۔) be its characteristic function. We call the function $\widehat{\psi}$ ( t1,…, tl ; z1,…, zl) = ${\sf E}\prod^l_{j=1}\widehat{\psi}(t_j, z_j)$ of arguments l∈ ℕ, t1, t2… ∈T, z1, z2∈ ℝ d the covaristic of the measure-valued random function (MVRF) ψ(۔, ۔). A general limit theorem for MVRF's in terms of covaristics is proved and applied to functions of the kind ψ n( t, B) = µ{ x : ξ n( t, x) ∈B}, where μ is a nonrandom finite measure and, for each n, ξ n is a time-dependent random field.
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