Search results for "Lipschitz function"
showing 3 items of 3 documents
Absolutely continuous functions with values in a Banach space
2017
Abstract Let Ω be an open subset of R n , n > 1 , and let X be a Banach space. We prove that α-absolutely continuous functions f : Ω → X are continuous and differentiable (in some sense) almost everywhere in Ω.
Sobolev and bounded variation functions on metric measure spaces
2014
International audience
Topics in calculus and geometry on metric spaces
2022
In this thesis we present an overview of some important known facts related to topology, geometry and calculus on metric spaces. We discuss the well known problem of the existence of a lipschitz equivalent metric to a given quasiultrametric, revisiting known results and counterexamples and providing some new theorems, in an unified approach. Also, in the general setting of a quasi-metric doubling space, suitable partition of unity lemmas allows us to obtain, in step two Carnot groups, the well known Whitney’s extension theorem for a given real function of class C^m defined on a closed subset of the whole space: this result relies on relevant properties of the symmetrized Taylor’s polynomial…