A joint generalization of Whitneyʼs C1 extension theorem and Aversa-Laczkovich-Preissʼ extension theorem

We prove a joint generalization of Whitneyʼs C1 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 Rn to a differentiable function on Rn with preserving the continuity of the derivative. Other results on C1 and differentiable extensions from “thick” subsets of Rn are also proved.