  In this paper, we first show that for a countable family of random elements
taking values in a partially ordered Polish space (POP), association (both
positive and negative) of all finite dimensional marginals implies that of the
infinite sequence. Our proof proceeds via Strassen's theorem for stochastic
domination and thus avoids the assumption of normally ordered on the product
space as needed for positive association in [Lindqvist 1988]. We use these
results to show on Polish spaces that finite dimensional negative association
implies negative association of the random measure and negative association is
preserved under weak convergence of random measures. The former provides a
simpler proof in the most general setting of Polish spaces complementing the
recent proofs in [Poinas et al. 2017] and [Lyons 2014] which restrict to point
processes in Euclidean spaces and locally compact Polish spaces respectively.
We also provide some examples of associated random measures which shall
illustrate our results as well.
