  Measuring inequalities in a multidimensional framework is a challenging
problem which is common to most field of science and engineering. Nevertheless,
despite the enormous amount of researches illustrating the fields of
application of inequality indices, and of the Gini index in particular, very
few consider the case of a multidimensional variable. In this paper, we
consider in some details a new inequality index, based on the Fourier
transform, that can be fruitfully applied to measure the degree of
inhomogeneity of multivariate probability distributions. This index exhibits a
number of interesting properties that make it very promising in quantifying the
degree of inequality in data sets of complex and multifaceted social phenomena.
