On dominations between measures of dependence (Q1092495)

This paper is best summarized by the authors' abstract: Suppose one has two measures of dependence between two or more families of random variables. One of the measures is said to ``dominate'' the other if the latter becomes arbitrarily small as the former becomes sufficiently small. A description is given of the entire pattern of dominations between arbitrary pairs of measures of dependence that are based on the usual norms of the bilinear form ``covariance''. Also, for a broader class of measures of dependence, some earlier ``domination inequalities'' are shown to be essentially sharp.