Rademacher's theorem in Banach spaces without RNP

Rok, strany: 2017, 1345 - 1358

We improve a Duda's theorem concerning metric and ${w^*}$-Gâteaux differentiability of Lipschitz mappings, by replacing the $\sigma$-ideal $\mathcal A$ of Aronszajn null sets [ARONSZAJN, N.: \textit{Differentiability of Lipschitzian mappings between Banach spaces}, Studia Math. \textbf{57} (1976), 147--190], with the smaller $\sigma$-ideal $\at$ of Preiss-Zajíček null sets [PREISS, D.---ZAJÍČEK, L.: \textit{Directional derivatives of Lipschitz functions}, Israel J. Math. \textbf{125} (2001), 1--27]. We also prove the inclusion $\tilde{C}^{o}\subset\at$, where $\tilde{C}^{o}$ is the $\sigma$-ideal of Preiss null sets [PREISS, D.: \textit{Gâteaux differentiability of cone-monotone and pointwise Lipschitz functions}, Israel J. Math. \textbf{203} (2014), 501--534].

ISO 690:

Bongiorno, D. 2017. Rademacher's theorem in Banach spaces without RNP. In Mathematica Slovaca, vol. 67, no.6, pp. 1345-1358. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0056

APA:

Bongiorno, D. (2017). Rademacher's theorem in Banach spaces without RNP. Mathematica Slovaca, 67(6), 1345-1358. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0056