2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77176Basic aspects of differential geometry can be extended to various non-classical settings: Lipschitz manifolds, rectifiable sets, sub-Riemannian manifolds, Banach manifolds, Weiner space, etc. Although the constructions differ, in each of these cases one can define a module of measurable 1-forms and a first-order exterior derivative. We give a general construction which applies to any metric space equipped with a sigma-finite measure and produces the desired result in all of the above cases. It also applies to an important class of Dirichlet spaces, where, however, the known first-order differential calculus in general differs from ours (although the two are related).42 pagesFunctional AnalysisDifferential Geometry58A10 (primary); 28A75, 28A80, 31C25, 46E15, 46L57, 46M20, 46M25, 53C60, 54E35, 58A15, 58A40, 58B20, 58G32, 60J60, 60J65 (secondary)text