A joint generalization of Whitneyʼs extension theorem and Aversa–Laczkovich–Preissʼ extension theorem

We prove a joint generalization of Whitneyʼs C 1 extension theorem and Aversa–Laczkovich–Preissʼ extension theorem. It can be roughly described as a theorem on extendibility of a differentiable function defined on a closed subset of R n to a differentiable function on R n with preserving the continuity of the derivative. Other results on C 1 and differentiable extensions from “thick” subsets of R n are also proved.