Inserted: 23 jan 2018
Last Updated: 17 nov 2020
Journal: Journal of Functional Analysis
We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and $C^1$ functions. This way we prove more directly a result by Lee and Naor and we generalize the $C^1$ extension theorem by Whitney to Banach spaces.