  The correlations in classical multi-component ionic mixtures with spatial
dimension $d\geq 2$ are studied by using a restricted grand-canonical ensemble
and the associated hierarchy equations for the correlation functions. Sum rules
for the first few moments of the two-particle correlation function are derived
and their dependence on $d$ is established. By varying $d$ continuously near
$d=2$ it is shown how the sum rules for the two-dimensional mixture are related
to those for mixtures at higher $d$.
