Inserted: 21 jul 2020
Last Updated: 20 jan 2022
Journal: Rend. Lincei Mat. Appl.
The intent of this short note is to extend real valued Lipschitz functions on metric spaces, while locally preserving the asymptotic Lipschitz constant. We then apply this results to give a simple and direct proof of the fact that Sobolev spaces on metric measure spaces defined with a relaxation approach \`a la Cheeger are invariant under isomorphism class of mm-structures.