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Countable Random Sets: Uniqueness in Law and Constructiveness

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  • Philip Herriger

    (Eberhard Karls Universität Tübingen)

Abstract

The first part of this article deals with theorems on uniqueness in law for σ-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two approaches on uniqueness theorems: first, the study of generators for σ-fields used in this context and, secondly, the analysis of hitting functions. The last section of this paper deals with the notion of constructiveness. We prove a measurable selection theorem and a decomposition theorem for constructive countable random sets, and study constructive countable random sets with independent increments.

Suggested Citation

  • Philip Herriger, 2013. "Countable Random Sets: Uniqueness in Law and Constructiveness," Journal of Theoretical Probability, Springer, vol. 26(3), pages 781-802, September.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:3:d:10.1007_s10959-012-0432-5
    DOI: 10.1007/s10959-012-0432-5
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