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Decompositions of Weakly Compact Valued Integrable Multifunctions

Author

Listed:
  • Luisa Di Piazza

    (Department of Mathematics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy)

  • Kazimierz Musiał

    (Institut of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland)

Abstract

We give a short overview on the decomposition property for integrable multifunctions, i.e., when an “integrable in a certain sense” multifunction can be represented as a sum of one of its integrable selections and a multifunction integrable in a narrower sense. The decomposition theorems are important tools of the theory of multivalued integration since they allow us to see an integrable multifunction as a translation of a multifunction with better properties. Consequently, they provide better characterization of integrable multifunctions under consideration. There is a large literature on it starting from the seminal paper of the authors in 2006, where the property was proved for Henstock integrable multifunctions taking compact convex values in a separable Banach space X . In this paper, we summarize the earlier results, we prove further results and present tables which show the state of art in this topic.

Suggested Citation

  • Luisa Di Piazza & Kazimierz Musiał, 2020. "Decompositions of Weakly Compact Valued Integrable Multifunctions," Mathematics, MDPI, vol. 8(6), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:863-:d:363169
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    References listed on IDEAS

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    1. Yilun Shang, 2013. "The Limit Behavior of a Stochastic Logistic Model with Individual Time-Dependent Rates," Journal of Mathematics, Hindawi, vol. 2013, pages 1-7, May.
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    Cited by:

    1. Adolfo Pimienta & Manuel Sanchis, 2023. "Continuous Selections and Extremally Disconnected Spaces," Mathematics, MDPI, vol. 11(4), pages 1-8, February.

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