Remarks on Fréchet differentiability of pointwise Lipschitz, cone-monotone and quasiconvex functions

Abstract

Some new generalizations of a deep result of J. Lindenstrauss and D.

Preiss on Gamma-almost everywhere Fréchet differentiability of Lipschitz functions on c_0 (and similar Banach spaces) are proved.

Keywords

• cone-monotone function
• Fréchet differentiability, Gateaux differentiability
• pointwise Lipschitz function
• Gamma-null set
• quasiconvex function
• separable reduction