On Intermediate Differentiability of Lipschitz Functions on Certain Banach Spaces

1991 ◽  
Vol 113 (3) ◽  
pp. 733 ◽  
Author(s):  
M. Fabian ◽  
D. Preiss
Keyword(s):  
Banach Spaces ◽  
Lipschitz Functions

Fr ´Echet Differentiability Except For Γ‎-Null Sets

2012 ◽  
Author(s):  
Joram Lindenstrauss ◽  
David Preiss ◽  
Tiˇser Jaroslav
Keyword(s):  
Banach Spaces ◽  
Common Point ◽  
Lipschitz Functions ◽  
Infinite Dimensional ◽  
Lipschitz Maps ◽  
Almost Everywhere ◽  
Fréchet Differentiability ◽  
Gateaux Derivatives ◽  
Frechet Differentiability ◽  
Porous Sets

This chapter gives an account of the known genuinely infinite dimensional results proving Fréchet differentiability almost everywhere except for Γ‎-null sets. Γ‎-null sets provide the only notion of negligible sets with which a Fréchet differentiability result is known. Porous sets appear as sets at which Gâteaux derivatives can behave irregularly, and they turn out to be the only obstacle to validity of a Fréchet differentiability result Γ‎-almost everywhere. Furthermore, geometry of the space may (or may not) guarantee that porous sets are Γ‎-null. The chapter also shows that on some infinite dimensional Banach spaces countable collections of real-valued Lipschitz functions, and even of fairly general Lipschitz maps to infinite dimensional spaces, have a common point of Fréchet differentiability.

Banach Spaces of Lipschitz Functions

2019 ◽  
pp. 365-556
Author(s):  
Ştefan Cobzaş ◽  
Radu Miculescu ◽  
Adriana Nicolae
Keyword(s):  
Banach Spaces ◽  
Lipschitz Functions
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