2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123332This paper explores the concept of reparametrization invariant norm (RPI-norm), that is any norm invariant under composition with diffeomorphisms. We prove the existence of an infinite family of RPI-norms, called standard RPI-norms, for which we exhibit both an integral and a discrete characterization. Our main result states that, for every one-time differentiable piecewise monotone function with compact support, its standard RPI-norms allow us to compute the value of any other RPI-norm of the same function. This is proved by using the standard RPI-norms in order to reconstruct the function up to reparametrization and an arbitrarily small error with respect to the total variation norm.50 pages, 10 figuresFunctional Analysis46E10; 46B20text