UNIFORM DISTRIBUTION AND ALGORITHMIC RANDOMNESS.
A seminal theorem due to Weyl [14] States that if (a) is any sequence of distinct integers, then, for almost every x ∈ ℝ, the sequence (ax) is uniformly distributed modulo one. In particular, for almost every x tu the unit interval, the sequence (ax) is uniformly distributed modulo one for every con...
| Publicado en: | Journal of Symbolic Logic Vol. 78; no. 1; pp. 334 - 345 |
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| Formato: | Artículo |
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Cambridge University Press
Mar2013
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=86872429&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 86872429 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Mar2013 vid: 78 iid: 1 pid: 15979 pub: Cambridge University Press artinfo: ui: 86872429 10.2178/jsl.7801230 ppf: 334 ppct: 11 formats: tig: atl: UNIFORM DISTRIBUTION AND ALGORITHMIC RANDOMNESS. aug: au: AVIGAD, JEREMY affil: DEPARTMENT OF PHILOSOPHY, CARNEGIE MELLON UNIVERSITY, PITTSBURGH, PA 15213, USA DEPARTMENT OF MATHEMATICAL SCIENCES, CARNEGIE MELLON UNIVERSITY, PITTSBURGH, PA 15213, USA su: Uniform distribution (Probability theory) Algorithmic randomness Integers Sequence analysis Stochastic analysis sug: subj: Uniform distribution (Probability theory) Algorithmic randomness Integers Sequence analysis Stochastic analysis ab: A seminal theorem due to Weyl [14] States that if (a) is any sequence of distinct integers, then, for almost every x ∈ ℝ, the sequence (ax) is uniformly distributed modulo one. In particular, for almost every x tu the unit interval, the sequence (ax) is uniformly distributed modulo one for every conspusable sequence (a) of distinct integers. Call such an x UD random. Here it is shown that every Schnorr random real is UD random, but there are Kurtz random reals that are not UD random. On the other hand, Weyl's theorem still holds relative to a particular effectively closed null set, so there are UD random reals that are not Kurtz random. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2013 holdings: @attributes: islocal: N |
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