On differential properties of mappings into a Banach space

• Date: 1997
• Main Authors: Bondar, A. V., Бондарь, А. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1997
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5023
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...