Israel Journal of Mathematics

, Volume 111, Issue 1, pp 191–201

Aronszajn null and Gaussian null sets coincide

Article

Abstract

We prove that in every separable Banach space the σ ideals of Aronszajn null sets, Gaussian null sets and cube null sets coincide.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    N. Aronszajn,Differentiability of Lipschitzian mappings between Banach spaces, Studia Mathematica57 (1976), 147–190.MATHMathSciNetGoogle Scholar
  2. [2]
    Y. Benyamini and J. Lindenstrauss,Geometric non-linear functional analysis, in preparation.Google Scholar
  3. [3]
    V. I. Bogachev,Negligible sets in locally convex spaces, (Russian) Matematicheskie Zametki36 (1984), 51–64. English translation: Mathematical Notes36 (1984), 519–526.MathSciNetGoogle Scholar
  4. [4]
    J. P. R. Christensen,Measure theoretic zero sets in infinite dimensional spaces and applications to differentiability of Lipschitz mappings, Actes du Deuxième Colloque d’Analyse Fonctionelle de Bordeaux (Univ. de Bordeaux, 1973), I, Publications du Départment de Mathématiques. Faculté des Sciences de Lyon. (Lyon)10 (1973), fasc. 2, 29–39.MATHMathSciNetGoogle Scholar
  5. [5]
    P. Mankiewicz,On the differentiability of Lipschitz mappings in Fréchet spaces, Studia Mathematica45 (1973), 15–29.MATHMathSciNetGoogle Scholar
  6. [6]
    R. R. Phelps,Gaussian null sets and differentiability of Lipschitz maps on Banach spaces, Pacific Journal of Mathematics77 (1978), 523–531.MATHMathSciNetGoogle Scholar
  7. [7]
    D. Preiss and J. Tišer,Two unexpected examples concerning differentiability of Lipschitz functions on Banach spaces, inGAFA Israel Seminar 92–94 (V. Milman and J. Lindenstrauss, eds.), Birkhäuser, Boston, 1995, pp. 219–238.Google Scholar

Copyright information

© Hebrew University 1999

Authors and Affiliations

  1. 1.Department of AnalysisLoránd Eötvös UniversityBudapestHungary

Personalised recommendations