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On the Strassen Theorem

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Analyse Convexe et Ses Applications

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 102))

Résumé

Many papers on Strassen theorem have been published since Strassen(s paper; CASTAING [1] [3], IOFFE LEVIN (§2 and §3), IONESCU TULCEA (A.), KÖNIG, LEVIN [1], MEYER, VALADIER [1]. Among the last extansions that of IOFFE LEVIN (§2) and KÖNIG suggest an abstract theorem. That is theorem 1, which we call abstract theorem because we obtain “pseudo-selections” in place of selections (the notion of pseudo-selection is also defined by GODET-THOBIE). It remains to find hypothesis which ensure that pseudo-selections can be replaced by selections. As in desintegration theorems we can either suppose the vertical space (here the vector space) to be separable, or that the horizontal space (here the measured space) has the strong lifting property. Thus we obtain two concrete Strassen theorems. The first one (theorem 2) is the same as in VALADIER [1]. The second one (theorem 4) is approximately the statement of IOFFE LEVIN (§3) but with a different proof. It seems (at the present time) that these two statements cover all generalizations, except the special one of CASTAING [2] [3].

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Authors
  1. Michel Valadier
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Editors and Affiliations

  1. Université Paris IX Dauphine Ceremade, Place du Maréchal-de-Lattre-de-Tassigny, 75775, Paris Cedex 16, France

    Jean-Pierre Aubin

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© 1974 Springer-Verlag Berlin Heidelberg

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Valadier, M. (1974). On the Strassen Theorem. In: Aubin, JP. (eds) Analyse Convexe et Ses Applications. Lecture Notes in Economics and Mathematical Systems, vol 102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00638-2_13

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  • DOI: https://doi.org/10.1007/978-3-662-00638-2_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07015-3

  • Online ISBN: 978-3-662-00638-2

  • eBook Packages: Springer Book Archive

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