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Finitely purely atomic measures: Coincidence and rigidity properties

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Abstract

This paper is a natural continuation of the paper [2] by the same author.

We shall prove that several coincidence and rigidity phenomena which usually do not appear are possible only in case the underlying measure space is trivial (i.e. is a finite union of atoms). Examples: coincidence of twoL p spaces, reflexivity ofL 1, Radon—Nikodym property ofL ∞, coincidence of Dunford, Pettis or Bochner integrability, coincidence of theL p space and of the weakL p space.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, Bucharest, Romania

    Ion Chiţescu

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  1. Ion Chiţescu
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Chiţescu, I. Finitely purely atomic measures: Coincidence and rigidity properties. Rend. Circ. Mat. Palermo 50, 455–476 (2001). https://doi.org/10.1007/BF02844425

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  • DOI: https://doi.org/10.1007/BF02844425

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