We study mappings f : (a, b) \to Y with finite dilation having Lebesgueintegrable majorant, where Y is a real normed vector space. We construct Lipschitz mapping f : (a, b) \to Y, \rm{dim}Y = \infty, which is nowhere differentiable but its graph has everywhere trivial contingent. We show that if the contingent of the graph of a mapping with finite dilation is a nontrivial space, then f is almost everywhere differentiable.
@article{348,
title = {On differentiability of mappings with finite dilation},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v62i0.348},
language = {EN},
url = {http://dml.mathdoc.fr/item/348}
}
Turowska, Małgorzata. On differentiability of mappings with finite dilation. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v62i0.348. http://gdmltest.u-ga.fr/item/348/