Geodesic
Smoothness of functions with respect to a set
Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 431-436 
V. A. Startsev. Smoothness of functions with respect to a set. Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 431-436. http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a9/
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     author = {V. A. Startsev},
     title = {Smoothness of functions with respect to a~set},
     journal = {Matemati\v{c}eskie zametki},
     pages = {431--436},
     year = {1974},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this note we consider the properties of functions which are smooth with respect to congruent sets. We find necessary and sufficient conditions which these congruent sets must satisfy in order that asymptotic differentiability, together with the smoothness relative to a set, will imply ordinary differentiability almost everywhere. We consider the case of measurable and continuous functions.