MARTIN-LÖF RANDOMNESS IN SPACES OF CLOSED SETS.
Algorithmic randomness was originally defined for Cantor space with the fair-coin measure. Recent work has examined algorithmic randomness in new contexts, in particular closed subsets of 2ɷ ([2] and [8]). In this paper we use the probability theory of closed set-valued random variables (RACS) to ex...
| Publicado en: | Journal of Symbolic Logic Vol. 80; no. 2; pp. 359 - 384 |
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| Formato: | Artículo |
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Cambridge University Press
Jun2015
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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=102228888&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 102228888 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Jun2015 vid: 80 iid: 2 pid: 15979 pub: Cambridge University Press artinfo: ui: 102228888 10.1017/jsl.2014.76 ppf: 359 ppct: 25 formats: tig: atl: MARTIN-LÖF RANDOMNESS IN SPACES OF CLOSED SETS. aug: au: AXON, LOGAN M. affil: DEPARTMENT OF MATHEMATICS GONZAGA UNIVERSITY 502 E. BOONE AVE. SPOKANE, WA 99258, USA su: Algorithms Set theory Probability theory Random variables Topological spaces sug: subj: Algorithms Set theory Probability theory Random variables Topological spaces keyword: Algorithmic randomness random closed sets ab: Algorithmic randomness was originally defined for Cantor space with the fair-coin measure. Recent work has examined algorithmic randomness in new contexts, in particular closed subsets of 2ɷ ([2] and [8]). In this paper we use the probability theory of closed set-valued random variables (RACS) to extend the definition of Martin-Löf randomness to spaces of closed subsets of locally compact, Hausdorff, second countable topological spaces. This allows for the study of Martin-Löf randomness in many new spaces, but also gives a new perspective on Martin-Löf randomness for 2ɷ and on the algorithmically random closed sets of [2] and [8]. The first half of this paper is devoted to developing the machinery of Martin-Löf randomness for general spaces of closed sets. We then prove some general results and move on to show how the algorithmically random closed sets of [2] and [8] fit into this new framework. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2015 holdings: @attributes: islocal: N |
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