Generalized Rademacher-Stepanov type theorem and applications (Q732872)

The author generalizes a theorem of Stepanov which provides a necessary and sufficient condition for almost everywhere differentiability of functions over Euclidean spaces. Precisely, an \(L^p\)-type generalization of the Stepanov theorem is proved and it is extended to the settings of Orlicz spaces. An application of this generalized Rademacher-Stepanov type theorem is given to the Sobolev and bounded variation maps with values into a metric space. It is shown that several generalized differentiability type theorems are valid for Sobolev maps acting from a Lipschitz manifold into a metric space. As a byproduct, it is shown that the Sobolev spaces of Korevaar-Schoen and Reshetnyak are equivalent.