A Note on Differentiability of Lipschitz Maps
نویسندگان
چکیده
منابع مشابه
On Fréchet differentiability of Lipschitz maps between Banach spaces
A well-known open question is whether every countable collection of Lipschitz functions on a Banach space X with separable dual has a common point of Fréchet differentiability. We show that the answer is positive for some infinite-dimensional X. Previously, even for collections consisting of two functions this has been known for finite-dimensional X only (although for one function the answer is...
متن کاملMetric differentiability of Lipschitz maps defined on Wiener spaces
This note is devoted to the differentiability properties of H-Lipschitz maps defined on abstract Wiener spaces and with values in metric spaces, so we start by recalling some basic definitions related to the Wiener space structure. Let (E, ‖ · ‖) be a separable Banach space endowed with a Gaussian measure γ. Recall that a Gaussian measure γ on E equipped with its Borel σ−algebra B is a probabil...
متن کاملOn Gâteaux Differentiability of Pointwise Lipschitz Mappings
Abstract. We prove that for every function f : X → Y , where X is a separable Banach space and Y is a Banach space with RNP, there exists a set A ∈ Ã such that f is Gâteaux differentiable at all x ∈ S(f) \ A, where S(f) is the set of points where f is pointwise-Lipschitz. This improves a result of Bongiorno. As a corollary, we obtain that every K-monotone function on a separable Banach space is...
متن کاملOn the Differentiability of Lipschitz Maps from Metric Measure Spaces to Banach Spaces
We consider metric measure spaces satisfing a doubling condition and a Poincaré inequality in the upper gradient sense. We show that the results of [Che99] on differentiability of real valued Lipschitz functions and the resulting bi-Lipschitz nonembedding theorems for finite dimensional vector space targets extend to Banach space targets having what we term a good finite dimensional approximati...
متن کاملLipschitz Maps on Trees
We introduce and study a metric notion for trees and relate it to a conjecture of Shelah [10] about the existence of a finite basis for a class of linear orderings.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Polish Academy of Sciences Mathematics
سال: 2010
ISSN: 0239-7269,1732-8985
DOI: 10.4064/ba58-3-8