Dentability and Differentiability

  • Marián Fabian
  • Petr Habala
  • Petr Hájek
  • Vicente Montesinos
  • Václav Zizler
Part of the CMS Books in Mathematics book series (CMSBM)


The main topic of the present chapter is the dentability of bounded sets and the closely related Radon–Nikodým property (RNP) of Banach spaces. This property has several equivalent characterizations and applications. In particular, Asplund spaces are characterized by the Radon–Nikodým property of their dual spaces. As another application, we show that Lipschitz mappings from separable Banach spaces into Banach spaces with RNP are at some points Gâteaux differentiable.


Banach Space Vector Measure Separable Banach Space Closed Unit Ball Lower Semicontinuous Function 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Marián Fabian
    • 1
  • Petr Habala
    • 2
  • Petr Hájek
    • 1
  • Vicente Montesinos
    • 3
  • Václav Zizler
    • 4
  1. 1.Mathematical Institute of the Academy of Sciences of the Czech RepublicPragueCzech Republic
  2. 2.Department of Mathematics, Faculty of Electrical EngineeringCzech Technical University in PraguePragueCzech Republic
  3. 3.Departamento de Matematica AplicadaUniversidad Politécnica de ValenciaValenciaSpain
  4. 4.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada

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