Effectively approximating measurable sets by open sets
نویسندگان
چکیده
منابع مشابه
Effectively approximating measurable sets by open sets
We answer a recent question of Bienvenu, Muchnik, Shen, and Vereshchagin. In particular, we prove an effective version of the standard fact from analysis which says that, for any ε > 0 and any Lebesgue-measurable subset of Cantor space, X ⊆ 2, there is an open set Uε ⊆ 2, Uε ⊇ X, such that μ(Uε) ≤ μ(X) + ε, where μ(Z) denotes the Lebesgue measure of Z ⊆ 2. More specifically, our main result sho...
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The lattice E of c.e. sets is a popular object of study in Computability Theory [So87]. A principal fact about this lattice is the undecidability of its first-order theory Th(E). Moreover, Th(E) is known [HN98] to be m-equivalent to the first-order arithmetic Th(N) where N := (ω; +,×). The lattice E may be considered as the lattice of effectively open subsets of the discrete topological space ω...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2012
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2012.01.011