6533b7d8fe1ef96bd126a532
RESEARCH PRODUCT
RADEMACHER'S THEOREM IN BANACH SPACES WITHOUT RNP
Donatella Bongiornosubject
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 sciencesMathematicsdescription
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].
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-11-01 |