On differential properties of mappings into a Banach space
We prove that the Rieffel sharpness condition for a Banach space E is necessary and sufficient for an arbitrary Lipschitz function f: [a, b]→E to be differentiable almost everywhere on a segment [a, b]. We establish that, in the case where the sharpness condition is not satisfied, the major part (in the category sense) of Lipschitz functions has no derivatives at any point of the segment [a, b].
English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 4, pp 550-560.
Citation Example: Bondar A. V. On differential properties of mappings into a Banach space // Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 500–509.