  We introduce mixed Segre numbers of ideals which generalize the notion of
mixed multiplicities of ideals of finite colength and show how many results on
mixed multiplicities can be extended to results on mixed Segre numbers. In
particular, we give a necessary and sufficient condition in terms of these
numbers for two ideals to have the same integral closure. Also, our theory
yields a new proof of a generalization of Rees' theorem that links the integral
closure of an ideal to its multiplicity. Finally, we give a quick application
of our results to Whitney equisingularity.
