Search results for "Rademacher's theorem"

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Rademacher Theorem for Fréchet spaces

2010

Abstract Let X be a separable Frechet space. In this paper we define a class A of null sets in X that is properly contained in the class of Aronszajn null sets, and we prove that a Lipschitz map from an open subset of X into a Gelfand-Frechet space is Gateaux differentiable outside a set belonging to A. This is an extension to Frechet spaces of a result (see [PZ]) due to D. Preiss and L. Zajicek.

Discrete mathematicsNull (mathematics)Space (mathematics)Lipschitz continuitySeparable spaceCombinatoricsRademacher's theoremMathematics (miscellaneous)Fréchet spaceSettore MAT/05 - Analisi MatematicaDifferentiable functionMetric differentialMathematicsLipschitz maps Gateaux differentiability Rademacher theorem.
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RADEMACHER'S THEOREM IN BANACH SPACES WITHOUT RNP

2017

Abstract We improve a Duda’s theorem concerning metric and w *-Gâteaux differentiability of Lipschitz mappings, by replacing the σ-ideal 𝓐 of Aronszajn null sets [ARONSZAJN, N.: Differentiability of Lipschitzian mappings between Banach spaces, Studia Math. 57 (1976), 147–190], with the smaller σ-ideal 𝓐 of Preiss-Zajíček null sets [PREISS, D.—ZAJÍČEK, L.: Directional derivatives of Lipschitz functions, Israel J. Math. 125 (2001), 1–27]. We also prove the inclusion C̃ o ⊂ 𝓐, where C̃ o is the σ-ideal of Preiss null sets [PREISS, D.: Gâteaux differentiability of cone-monotone and pointwise Lipschitz functions, Israel J. Math. 203 (2014), 501–534].

Pure mathematicsRademacher's theoremSettore MAT/05 - Analisi MatematicaGeneral Mathematics010102 general mathematics0103 physical sciencesBanach spaceLipschitz maps Radon-Nikodym property metric Gateaux differentiability w-Gòateaux differentiability.010307 mathematical physics0101 mathematics01 natural sciencesMathematics
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