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1دورية أكاديمية
المؤلفون: Ross, David A.
الوصف: S-measures are Loeb measures restricted to the sigma algebra generated by standard sets. This paper gives new extensions of the S-measure machinery, with applications to standard measure theory.
وصف الملف: application/pdf
العلاقة: http://projecteuclid.org/euclid.jsl/1388954005Test; J. Symbolic Logic 78, iss. 4 (2013), 1247-1256
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2دورية أكاديمية
المؤلفون: Loeb, Peter A., Ross, David A.
الوصف: Let $(X_i,{\mathscr B}_i,m_i)$ $(i\in{\mathbb N})$ be a sequence of regular Borel measure spaces. There is a Borel measure $\mu$ on $\prod_{i\in{\mathbb N}}{X_i}$ such that if $K_i\subseteq X_i$ is compact for all $i\in{\mathbb N}$ and $\prod_{i\in{\mathbb N}}{m_i(K_i)}$ converges, then $\mu({\prod_{i\in{\mathbb N}}{K_i}})=\prod_{i\in{\mathbb N}}{m_i(K_i)}$.
وصف الملف: application/pdf
العلاقة: https://projecteuclid.org/euclid.ijm/1258138311Test; Illinois J. Math. 49, no. 1 (2005), 153-158
الإتاحة: https://doi.org/10.1215/ijm/1258138311Test
https://projecteuclid.org/euclid.ijm/1258138311Test -
3دورية أكاديمية
المؤلفون: Ross, David
العلاقة: http://projecteuclid.org/euclid.jsl/1183743416Test; J. Symbolic Logic 55, iss. 3 (1990), 1233-1242
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4دورية أكاديمية
المؤلفون: Ross, David
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.
وصف الملف: application/pdf
العلاقة: http://projecteuclid.org/euclid.aop/1176992459Test; Ann. Probab. 14, no. 3 (1986), 1064-1069
الإتاحة: https://doi.org/10.1214/aop/1176992459Test
http://projecteuclid.org/euclid.aop/1176992459Test
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