منابع مشابه
Metric 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...
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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...
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In this paper we prove the differentiability of Lipschitz maps X → V , where X is a complete metric measure space satisfying a doubling condition and a Poincaré inequality, and V denotes a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional derivatives in the direct...
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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...
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We prove that a compact metric space (or more generally an analytic subset of a complete separable metric space) of Hausdorff dimension bigger than k can be always mapped onto a k-dimensional cube by a Lipschitz map. We also show that this does not hold for arbitrary separable metric spaces. As an application we essentially answer a question of Urbański by showing that the transfinite Hausdorff...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2013
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788713000360