Stationary countable dense random sets
UNSPECIFIED. (2000) Stationary countable dense random sets. ADVANCES IN APPLIED PROBABILITY, 32 (1). pp. 86-100. ISSN 0001-8678Full text not available from this repository.
We study the probability theory of countable dense random subsets of (uncountably infinite) Polish spaces. It is shown that if such a set is stationary with respect to a transitive (locally compact) group of symmetries then any event which concerns the random set itself (rather than accidental details of its construction) must have probability zero or one. Indeed the result requires only quasi-stationarity (null-events stay null under the group action). In passing, it is noted that the property of being countable does not correspond to a measurable subset of the space of subsets of an uncountably infinite Polish space.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||ADVANCES IN APPLIED PROBABILITY|
|Publisher:||APPLIED PROBABILITY TRUST|
|Official Date:||March 2000|
|Number of Pages:||15|
|Page Range:||pp. 86-100|
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