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Ein Masstheoretisches Marginalproblem

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Abstract

Let ((Xi, Ki, μi) iεI) be a family of normed measure spaces. We study the extremal points of the convex set F of normed measures on the product of ((Xi, Ki): iεI) with the marginal measures μi. We give a construction principle for extremal points. If μi is the Lebesgue measure on [0, 1] and I is countable, we prove by using this principle that the set of extremal points of F is weakly dense in F. Finally we give a necessary and some sufficient conditions for extremal points in the case that I={1,2} and μi is the Lebesgue measure on [0,1] for i=1,2.

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Authors and Affiliations

  1. Mathematisches Institut der Universität, Theresienstr. 39, D-8, München 2

    Ulrich Oppel

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  1. Ulrich Oppel
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Oppel, U. Ein Masstheoretisches Marginalproblem. Manuscripta Math 10, 359–377 (1973). https://doi.org/10.1007/BF01527259

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