Limit theorem for associated random measures

In this paper, we investigate a limit theorem for a nonstatioaryd-parameter array of associated random variables applying the criterion of the tightness condition in Donsker,M1951]. Our resuits imply an extension to the nonstatioary case of Convergence of Probability Measure of Billingsley.P 1968]. and analogous results for thed-dimensional associated random measure. These results are also applied to show a new limit theorem for Poisson cluster random measures.