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Compactness in Spaces of Inner Regular Measures and a General Portmanteau Lemma

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  • Volker Krätschmer

Abstract

This paper may be understood as a continuation of Topsøe’s seminal paper ([16]) to characterize, within an abstract setting, compact subsets of finite inner regular measures w.r.t. the weak topology. The new aspect is that neither assumptions on compactness of the inner approximating lattices nor nonsequential continuity properties for the measures will be imposed. As a providing step also a generalization of the classical Portmanteau lemma will be established. The obtained characterizations of compact subsets w.r.t. the weak topology encompass several known ones from literature. The investigations rely basically on the inner extension theory for measures which has been systemized recently by König ([8], [10],[12]).

Suggested Citation

  • Volker Krätschmer, 2006. "Compactness in Spaces of Inner Regular Measures and a General Portmanteau Lemma," SFB 649 Discussion Papers SFB649DP2006-081, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2006-081
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-081.pdf
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    Cited by:

    1. Volker Krätschmer, 2007. "On s-additive robust representation of convex risk measures for unbounded financial positions in the presence of uncertainty about the market model," SFB 649 Discussion Papers SFB649DP2007-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Inner Premeasures; Weak Topology; Generalized Portmanteau Lemma.;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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