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arXiv · 1206.6227

Countable Random Sets: Uniqueness in Law and Constructiveness

Philip Herriger
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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 will prove a measurable selection theorem and a decomposition theorem for constructive countable random sets, and study constructive countable random sets with independent increments.

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Philip Herriger. 2012-07-23. Countable Random Sets: Uniqueness in Law and Constructiveness. https://doi.org/10.1007/s10959-012-0432-5

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