RADEMACHER'S THEOREM IN BANACH SPACES WITHOUT RNP

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Abstract

We improve a Duda's theorem concerning metric and w-Gateaux differentiability ofLipschitz mappings, by replacing the -ideal A of Aronszajn null sets [ARONSZAJN, N.: Differentiabilityof Lipschitzian mappings between Banach spaces, Studia Math. 57 (1976), 147{190], with thesmaller -ideal ~ A of Preiss-Zajcek null sets [PREISS, D.|ZAJI CEK, L.: Directional derivatives ofLipschitz functions, Israel J. Math. 125 (2001), 1{27]. We also prove the inclusion C^{~o} \subset A^~, where C^{~o}is the \sigma-ideal of Preiss null sets [PREISS, D.: Gateaux differentiability of cone-monotone and pointwiseLipschitz functions, Israel J. Math. 203 (2014), 501{534].
Original languageEnglish
Pages (from-to)1345-1358
Number of pages14
JournalMathematica Slovaca
Volume67
Publication statusPublished - 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics

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