2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67323Lyons' Rough Path theory is currently formulated in p-variation topology. We extend his main-result, the Universal Limit Theorem, to a stronger Hoelder topology. Several approximations to Brownian Rough Paths are studied. As application of our approach, we obtain the celebrated support theorem (in Hoelder-topology) as immediate (!) corollary.Probability60H99Continuity of the Ito-Map for Hoelder rough paths with applications to the support theorem in Hoelder normtext