2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139341A classical result of Kemperman gives a complete recursive description of the structure of those subsets $A$ and $B$ of an abelian group that fail to satisfy the triangle inequality, i.e., $|A+B|<|A|+|B|$. In this paper, we achieve the complete description in the case when equality holds: $|A+B|=|A|+|B|$.CombinatoricsNumber Theory11P70text