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On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts

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Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

Abstract

The aim of this paper is to give a brief summary of the Pettis and Bochner integrals, how they are related, how they are generalized to the set-valued setting and the canonical Banach spaces of bounded maps between Banach spaces that they generate. The main tool that we use to relate the Banach space-valued case to the set-valued case, is the Rådström embedding theorem.

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Author information

Authors and Affiliations

  1. School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, P O WITS 2050, South Africa

    Coenraad C. A. Labuschagne

  2. Dipartimento di Matematica e Informatica, Università Degli Studi Di Palermo, Via Archirafi, 34, 90123, Palermo, Italy

    Valeria Marraffa

Authors
  1. Coenraad C. A. Labuschagne
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  2. Valeria Marraffa
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Labuschagne, C.C.A., Marraffa, V. (2011). On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_6

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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