منابع مشابه
Isomorphisms for Convergence Structures. II. Borel Spaces and Infinite Measures
In [10] we introduced a new notion of isomorphisms for topological measure spaces, which preserve almost sure continuity of mappings, almost sure convergence of random variables, and weak convergence of probability measures. The main thrust of that paper is the construction of an isomorphism from a Polish space with a nonatomic Borel probability measure to the unit Lebesgue interval (I, *). App...
متن کاملLoeb Measures and Borel Algebras
It is shown that a measurable function from an atomless Loeb probability space (Ω,A, P ) to a Polish space is at least continuum-to-one valued almost everywhere. It follows that there is no injective mapping h : [0, 1] → Ω such that h([a, b]) is Loeb measurable for each 0 ≤ a < b ≤ 1 and P (h([0, 1])) > 0. Thus, when an atomless Loeb measurable algebra on an internal set of cardinality continuu...
متن کاملBorel Extensions of Baire Measures in Zfc
We prove: (1) Every Baire measure on the Kojman-Shelah Dowker space [10] admits a Borel extension. (2) If the continuum is not a real-valued measurable cardinal then every Baire measure on the M. E. Rudin Dowker space [16] admits a Borel extension. Consequently, Balogh’s space [3] remains as the only candidate to be a ZFC counterexample to the measure extension problem of the three presently kn...
متن کاملOn Separable Supports of Borel Measures
Some properties of Borel measures with separable supports are considered. In particular, it is proved that any σ-finite Borel measure on a Suslin line has a separable supports and from this fact it is deduced, using the continuum hypothesis, that any Suslin line contains a Luzin subspace with the cardinality of the continuum. Let E be a topological space. We say that the space E has the propert...
متن کاملDynamical Borel-Cantelli lemmas for Gibbs measures
Let T : X 7→ X be a deterministic dynamical system preserving a probability measure μ. A dynamical Borel-Cantelli lemma asserts that for certain sequences of subsets An ⊂ X and μ-almost every point x ∈ X the inclusion Tnx ∈ An holds for infinitely many n. We discuss here systems which are either symbolic (topological) Markov chain or Anosov diffeomorphisms preserving Gibbs measures. We find suf...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1996
ISSN: 0166-8641
DOI: 10.1016/0166-8641(95)00089-5