Effectively closed sets of measures and randomness
نویسندگان
چکیده
منابع مشابه
Effectively closed sets of measures and randomness
We show that if a real x ∈ 2 is strongly Hausdorff Hh-random, where h is a dimension function corresponding to a convex order, then it is also random for a continuous probability measure μ such that the μ-measure of the basic open cylinders shrinks according to h. The proof uses a new method to construct measures, based on effective (partial) continuous transformations and a basis theorem for Π...
متن کاملEffectively Closed Set of Measures and Randomness
We show that if a real x ∈ 2 is Hausdorff H-random, where h is an order function, then it is also random for a continuous probability measure μ such that the μ-measure of the basic open cylinders shrinks according to h. We use this result to derive a characterization of effective Hausdorff dimension similar to Frostman’s Theorem.
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We study inversions of the jump operator on Π1 classes, combined with certain basis theorems. These jump inversions have implications for the study of the jump operator on the random degrees—for various notions of randomness. For example, we characterize the jumps of the weakly 2-random sets which are not 2-random, and the jumps of the weakly 1-random relative to 0′ sets which are not 2-random....
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2008
ISSN: 0168-0072
DOI: 10.1016/j.apal.2008.06.015