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Advances in Mathematical Economics pp 17–37Cite as

Convergences in L 1X (μ)

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Part of the book series: Advances in Mathematical Economics ((MATHECON,volume 1))

Summary

We present new modes of convergences for bounded sequences in the space L 1X (μ) of Bochner integrable functions over a complete probability space (Ω, F, μ) with values in Banach space X via the convergence of its truncated subsequences as well as we give several characterizations of weak compactness and conditionally weak compactness in L 1X (μ). New results involving subsets in L 1X (μ) which are closed in measure are obtained and also the characterizations of the Banach space X in terms of these modes of convergence.

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Author information

Authors and Affiliations

  1. Département de Mathématiques, Case 051, Université Montpellier II, F-34095, Montpellier cedex 5, France

    Charles Castaing

  2. Faculté des Sciences Ben M’sik, Département de Mathématiques, Université Hassan II Mohamedia, BP 7955, Ben M’sik, Casablanca, Maroc

    Mohamed Guessous

Authors
  1. Charles Castaing
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  2. Mohamed Guessous
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Editor information

Editors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-0041, Japan

    Shigeo Kusuoka (Professor) (Professor)

  2. Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan

    Toru Maruyama (Professor) (Professor)

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© 1999 Springer-Verlag

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Castaing, C., Guessous, M. (1999). Convergences in L 1X (μ) . In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 1. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65895-5_3

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  • DOI: https://doi.org/10.1007/978-4-431-65895-5_3

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-65897-9

  • Online ISBN: 978-4-431-65895-5

  • eBook Packages: Springer Book Archive

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