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Prämessbare Funktionen

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Abstract

Let (X,A,p) be a complete probability space. A function f: X→ℝ is called premeasurable, if there is a measure extension of p defined on the б-algebra generated byA and the function f. Several classes of premeasurable functions are studied here. This paper is a continuation of Bierlein's investigations in [2], [3] and [4]. The basic ideas and notations can be found there.

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Literatur

  1. AUMANN, R.J.: Measurable utility and measurable choice theorem, Colloques internat. Centre nat. Rech. Sci.171, 15–26 (1969)

    Google Scholar 

  2. BIERLEIN, D.: Der Graph meßbarer Funktionen mit abstraktem Definitionsbereich, Math. Z.76, 468–471 (1961)

    Google Scholar 

  3. BIERLEIN, D.: Über die Fortsetzung von Wahrscheinlichkeitsfeldern, Z. Wahrscheinlichkeitstheorie verw. Gebiete1, 28–46 (1962)

    Google Scholar 

  4. BIERLEIN, D.: Die Konstruktion eines Maßes μ ..., Z. Wahrscheinlichkeitstheorie verw. Gebiete1, 126–140 (1962)

    Google Scholar 

  5. BOURBAKI, N.: Éléments de mathématique, Fasc. XXXV, Livre VI, Intégration, Chap. IX, Paris: Hermann 1969

    Google Scholar 

  6. HALMOS, P.R.: Measure Theory, Princeton: Van Nostrand 1950

    Google Scholar 

  7. LEHN, J.: Maßfortsetzungen und Aumann's Selektionstheorem, Z. Wahrscheinlichkeitstheorie verw. Gebiete35, 265–268 (1976)

    Google Scholar 

  8. OXTOBY, J.C.: Measure and Category, Graduate Texts in Mathematics2, Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  9. ULAM, S.: Zur Maßtheorie in der allgemeinen Mengenlehre, Fundamenta Math.16, 140–150 (1930)

    Google Scholar 

  10. YERSHOV, M.P.: Extension of measures. Stochastic equations. Lecture Notes in Mathematics330, 516–526, Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  11. YERSHOV (ERSHOV), M.P.: Extension of measures and stochastic equations, Theor. Probability Appl.19, 431–444 (1974)

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut II, Universität Karlsruhe Englerstraße, D-7500, Karlsruhe, Bundesrepublik Deutschland

    Jürgen Lehn

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  1. Jürgen Lehn
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Lehn, J. Prämessbare Funktionen. Manuscripta Math 20, 141–152 (1977). https://doi.org/10.1007/BF01170722

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  • DOI: https://doi.org/10.1007/BF01170722

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