This paper presents general conditions under which a subfamily may be selected from an infinite family of nonnegative, finitely additive measures such that this subfamily has the same cardinality as the original family, and such that the members of this subfamily are, in a certain sense, dis jointly supported. The generalized continuum hypothesis is required for the general result, but not for a special case of this result which had previously been obtained by Rosenthal, and for which the present techniques yield a much shorter proof.