منابع مشابه
Borel Generators
We use the notion of Borel generators to give alternative methods for computing standard invariants, such as associated primes, Hilbert series, and Betti numbers, of Borel ideals. Because there are generally few Borel generators relative to ordinary generators, this enables one to do manual computations much more easily. Moreover, this perspective allows us to find new connections to combinator...
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For a continuous action of a countable discrete group G on a Polish space X, a countable Borel partition P of X is called a generator if GP ∶= {gP ∶ g ∈ G,P ∈ P} generates the Borel σ-algebra of X. For G = Z, the Kolmogorov–Sinai theorem gives a measuretheoretic obstruction to the existence of finite generators: they do not exist in the presence of an invariant probability measure with infinite...
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We show that there is a complete, consistent Borel theory which has no “Borel model” in the following strong sense: There is no structure satisfying the theory for which the elements of the structure are equivalence classes under some Borel equivalence relation and the interpretations of the relations and function symbols are Borel in the natural sense. We also investigate Borel isomorphisms be...
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We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
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The Borel-Cantelli Lemma is very important in the probability theory. In this paper, we first describe the general case of the Borel-Cantelli Lemma. The first part of this lemma, assuming convergence and the second part includes divergence and independence assumptions. In the following, we have brought generalizations of the first and second part of this lemma. In most generalizat...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2010.09.042