The robustness of the generalized Gini index

Abstract In this paper, we introduce a map $$\varPhi $$ Φ , which call zonoid from the space of all non-negative, finite Borel measures on $${\mathbb {R}}^n$$ R n with first moment to zonoids . This map, connecting measure theory theory, allows slightly generalize Gini volume introduced, in context Industrial Economics, by Dosi (J Ind Econ 4:875–907, 2016). volume, based geometric notion zonoid, is introduced as heterogeneity among firms an industry and it turned out be quite interesting index multidimensional generalization well-known broadly used index. By exploiting mathematical offered our definition, prove continuity which, turn, validity SLLN-type theorem for generalized and, hence, volume. Both results, SLLN theorem, are particularly useful when dealing huge amount data.