A class of second-order stationary random measures

Experimental measurements associated with n-dimensional regions or “plots” are regarded as observations on random variables indexed by the bounded Borel subsets of Rⁿ, these random variables having finite second moments and satisfying a certain additivity property. Further assumptions concerning the stationary and continuity of the first two moments allow spectral representations to be derived which are analogous to those already in the literature on second-order stationary random measures.