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On the Lyapunov convexity theorem with appications to sign-embeddings

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Abstract

It is proved (Theorem 1) that for a Banach space X the following assertions are equivalent: (1) the range of every X- valued σ- additive nonatomic measure of finite variation possesses a convex closure; (2) L1 does not signembed in X.

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Authors and Affiliations

  1. Kharkiv University, USSR

    V. M. Kadets & M. M. Popov

  2. Zaporizhzhia University, USSR

    V. M. Kadets & M. M. Popov

Authors
  1. V. M. Kadets
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  2. M. M. Popov
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Published in Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1192–1200, September, 1992.

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Kadets, V.M., Popov, M.M. On the Lyapunov convexity theorem with appications to sign-embeddings. Ukr Math J 44, 1091–1098 (1992). https://doi.org/10.1007/BF01058369

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  • DOI: https://doi.org/10.1007/BF01058369

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