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Decomposition theorems

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Abstract

The countable-decomposition theorem for linear functionals has become a useful tool in the theory of representing measures (see [4–7]). The original proof of this theorem was based on a rather involved study of extreme points in the state space of a convex cone. Recently M. Neumann [9] gave an independent proof using a refined form of Simons convergence lemma and Choquet's theorem. In this paper a (relatively) short proof of an extension (to a more abstract situation) of the countable-decomposition theorem is given. Furthermore a decomposition criterion is obtained which even works in the case when not all states are decomposable. All the work is based on a complete characterization of those states which are partially decomposable with respect to a given sequence of sublinear functionals.

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References

  1. Alfsen, E.M.: Compact convex sets and boundary Integrals. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  2. Bauer, H.: Wahrscheinlichkeitstheorie und Grundzüge der Maßtheorie. Berlin: de Gruyter 1968

    Google Scholar 

  3. Fuchssteiner, B.: Sandwich theorems and lattice Semigroups. J. functional Analysis 16, 1–14 (1974)

    Google Scholar 

  4. Fuchssteiner, B.: Maße auf σ-kompakten Räumen. Math.Z. 142, 185–190 (1975)

    Google Scholar 

  5. Fuchssteiner, B.: When does the Riesz representation theorem hold? Arch.Math. 28, 173–181 (1977)

    Google Scholar 

  6. Fuchssteiner, B.: Signed representing measures. Arch.Math. (1977)

  7. Fuchssteiner, B. and J.D. Maitland Wright: Representing isotone operators on cones.(1976) to appear in: Quart.J.Math. Oxford

  8. König, H.: Sublineare Funktionale. Arch.Math. 23, 500–508 (1972)

    Google Scholar 

  9. Neumann, M.: Varianten zum Konvergenzsatz von Simons und Anwendungen in der Choquettheorie. Arch.Math. 28, 182–192 (1977)

    Google Scholar 

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Author notes

  1. B. Fuchssteiner

    Present address: Fachbereich Mathematik Gesamthochschule, D-479, Paderborn, Germany

Authors and Affiliations

  1. Dept. de mathématiques, Ecole Polytechnique Fédérale de Lausanne, 61 Av de Cour, CH-1007, Lausanne

    B. Fuchssteiner

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  1. B. Fuchssteiner
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Fuchssteiner, B. Decomposition theorems. Manuscripta Math 22, 151–164 (1977). https://doi.org/10.1007/BF01167858

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  • DOI: https://doi.org/10.1007/BF01167858

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