دورية أكاديمية
Random Sets Without Separability
| العنوان: | Random Sets Without Separability |
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| المؤلفون: | Ross, David |
| بيانات النشر: | The Institute of Mathematical Statistics |
| سنة النشر: | 1986 |
| المجموعة: | Project Euclid (Cornell University Library) |
| مصطلحات موضوعية: | Random set, Choquet capacity, Konig's lemma, 60D05, 60G57, 60G55 |
| الوصف: | Suppose $\mathscr{V}$ and $\mathscr{F}$ are sets of subsets of $X$, for some fixed $X$. We apply Konig's lemma from infinitary combinatorics to prove that if $\mathscr{V}$ and $\mathscr{F}$ satisfy some simple closure properties, and $T$ is a Choquet capacity on $X$, then there is a probability measure on $\mathscr{F}$ such that for every $V \in \mathscr{F}, \{F \in \mathscr{F}: F \cap V \neq \varnothing\}$ is measurable with probability $T(V)$. This extends the well-known case when $\mathscr{F}$ and $\mathscr{V}$ are the closed (respectively, open) subsets of a second countable Hausdorff space $X$. The result enables us to define a general notion of "random measurable set"; for example, we can build a point process with Poisson distribution on any infinite (possibly nontopological) measure space. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0091-1798 |
| العلاقة: | http://projecteuclid.org/euclid.aop/1176992459Test; Ann. Probab. 14, no. 3 (1986), 1064-1069 |
| DOI: | 10.1214/aop/1176992459 |
| الإتاحة: | https://doi.org/10.1214/aop/1176992459Test http://projecteuclid.org/euclid.aop/1176992459Test |
| حقوق: | Copyright 1986 Institute of Mathematical Statistics |
| رقم الانضمام: | edsbas.717C9F03 |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 00911798 |
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| DOI: | 10.1214/aop/1176992459 |