  The main aim of this work is to compare two Borel measures thorough their
moment matrices using a new notion of smallest and largest generalized
eigenvalues. With this approach we provide information in problems as the
localization of the support of a measure. In particular, we prove that if a
measure is comparable in an algebraic way with a measure in a Jordan curve then
the curve is contained in its support. We obtain a description of the convex
envelope of the support of a measure via certain Rayleigh quotients of certain
infinite matrices. Finally some applications concerning polynomial
approximation in mean square are given, generalizing the results in [9].
