Multilevel interterritorial convergence and additive multidimensional inequality decomposition

----------------------------In this paper we justify the use of the between-groups S-convex relative inequality to measure interregional convergence, within an axiomatic normative context. In addition, the use of additive decomposable inequality indices makes the additive multidimensional (and multilevel) inequality decomposition possible, and help us better understand the evolution of the betweenand the withingroups inequality terms (and convergence) when the number of regions increases. We have detected a weak interterritorial divergence process in Spain in the period 1980-1995 using the Eurostat per capita GDP data at all levels, although it is mainly generated at the broad NUTS 1 areas, which is compatible with high level of increasing polarization at this level.