  In this paper, we consider a coherent theory about the asymptotic
representations for a family of inequality indices called Theil-Like Inequality
Measures (TLIM), within a Gaussian field. The theory uses the functional
empirical process approach. We provide the finite-distribution and uniform
asymptotic normality of the elements of the TLIM class in a unified approach
rather than in a case by case one. The results are then applied to some UEMOA
countries databases.
