Recent advances in the theory of metric measures spaces on the one hand, and of sub-Riemannian ones on the other hand, suggest the possibility of a "great unification" of Riemannian and sub-Riemannian geometries in a comprehensive framework of synthetic Ricci curvature lower bounds, as put forth in Villani (2019). With the aim of achieving such a unification program, in this paper we initiate the study of gauge metric measure spaces.
