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Zur Integrationstheorie über bewerteten Körpern und der Darstellung des Biduals von 65-165-165-1

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Abstract

The aim of this paper is to prove several theorems of Radon-Nikodym-type, which hold both in real and non-archimedean integration theory. As an application of these theorems and of the classical Radon-Nikodym theorem, we give a description of the second dual\(\mathbb{D}\)(X,ℂ) of the space

of all continuous complex valued functions on the locally compact space X, which vanish at infinity.

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Literatur

  1. BOURBAKI, N.: General Topology, part 1,2; Paris: Hermann 1966.

    Google Scholar 

  2. BOURBAKI, N.: Espaces vectoriels topologiques Chap. I, II; Paris 1966.

  3. BOURBAKI, N.: Intégration, Chap. I–IV; 2. Aufl. Paris Hermann 1965.

    Google Scholar 

  4. BOURBAKI, N. Intégration, Chap V; 2. Aufl. Paris: Hermann 1967.

    Google Scholar 

  5. BOURBAKI, N.: Intégration, Chap. IX; Paris: Hermann 1969.

    Google Scholar 

  6. FLORET, K. und J. WLOKA: Einführung in die Theorie der lokal konvexen Räume. Lecture Notes in Math. 56; Berlin-Heidelberg-New York: Springer 1968.

    Google Scholar 

  7. JACOBSON, N.: Lectures in Abstract Algebra III; Princeton: van Nostrand 1964.

    Google Scholar 

  8. MONNA, A. F. und T. A. SPRINGER: Intégration non-archimédienne I, II; Proc. Kon. Ned. Akad. v. Wetensch.A66, (Indag. Math.25) 634–642, 643–653 (1963).

    Google Scholar 

  9. SAKAI, S.: C*-Algebras and W*-Algebras; Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60; Berlin-Heidelberg-New York: Springer 1971.

    Google Scholar 

  10. SCHIKHOF, W. H.: Non-archimedean harmonic analysis; Thesis, Nijmegen 1967.

  11. SCHIKHOF, W. H.: A Radon-Nikodym theorem for nonarchimedean integrals and absolutely continuous measures on groups; Proc. Kon. Ned. akad. v. Wetensch.A74, (Indag. Math.33) 78–85 (1971).

    Google Scholar 

  12. TIEL, J. van: Espaces localement K-convexes I, II, III; Proc. Kon. Ned. Akad. v. Wetensch.A68, (Indag. Math.27) 249–258, 259–272, 273–289 (1965).

    Google Scholar 

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Authors and Affiliations

  1. Fachbereich Mathematik der Universität, Postfach 733, 775, Konstanz

    Hans F. de Groote

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  1. Hans F. de Groote
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Die vorliegende Arbeit entstand aus dem ersten Teil meiner Dissertation über nicht-archimedische Integrationstheorie. Herrn Prof. Dr. G. Neubauer und Herrn Dr. F. Lorenz sei an dieser Stelle für Anregungen und kritische Diskussionen herzlich gedankt.

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de Groote, H.F. Zur Integrationstheorie über bewerteten Körpern und der Darstellung des Biduals von 65-165-165-1. Manuscripta Math 10, 65–89 (1973). https://doi.org/10.1007/BF01677008

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  • DOI: https://doi.org/10.1007/BF01677008

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