منابع مشابه
Stationary countable dense random sets
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-...
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A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are Brownian local minima and unordered infinite sample. They are identically distributed; the former ad hoc proof of this fact is now superseded by a general result. Introduction Random dense countable sets arise naturally from various probabilistic models. Their examination is impede...
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We present several forcing posets for adding a non-reflecting stationary subset of Pω1 (λ), where λ ≥ ω2. We prove that PFA is consistent with dense non-reflection in Pω1 (λ), which means that every stationary subset of Pω1 (λ) contains a stationary subset which does not reflect to any set of size א1. If λ is singular with countable cofinality, then dense non-reflection in Pω1 (λ) follows from ...
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We compare two examples of random dense countable sets, Brownian local minima and unordered uniform infinite sample. They appear to be identically distributed. A framework for such notions is proposed. In addition, random elements of other singular spaces (especially, reals modulo rationals) are considered. Introduction For almost every Brownian path ω = (bt)t∈[0,1] on [0, 1], the set (0.1) Mω ...
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We show that all sufficiently nice λ-sets are countable dense homogeneous (CDH). From this fact we conclude that for every uncountable cardinal κ ≤ b there is a countable dense homogeneous metric space of size κ. Moreover, the existence of a meager in itself countable dense homogeneous metric space of size κ is equivalent to the existence of a λ-set of size κ. On the other hand, it is consisten...
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2000
ISSN: 0001-8678,1475-6064
DOI: 10.1239/aap/1013540024