In a previous paper (A multivariate notion of association, with a reliability application) random variables T1,T2, ..., Tn were defined to be associated if each pair of non-decreasing functions F(T1,T2, ..., Tn), G(T1,T2, ..., Tn) have a non-negative covariance. The properties of this definition were studied in the case that T1,T2, ..., Tn are finitely discrete, and a sample application to reliability theory was discussed. In the present paper several equivalent definitions of the same notion of association for unrestricted T1,T2, ..., Tn are treated. The properties previously obtained, i.e. that association is preserved under the operations of extracting subsets, pooling independent sets, and forming sets of non-decreasing functions, are shown to hold in general. In addition, association is shown to be preserved under limits in distribution. Some additional applications of association are discussed, e.g. previously published results of A.W. Kimball and H. Robbins are obtained. (Author).