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Translating the Cantor set by a random real

We determine the constructive dimension of points in random translates of the Cantor set. The Cantor set ``cancels randomness'' in the sense that some of its members, when added to Martin-Löf random reals, identify a point with lower constructive dimension than the random itself. In parti...

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Hauptverfasser: Dougherty, Randall (VerfasserIn) , Lutz, Jack (VerfasserIn) , Mauldin, R. Daniel (VerfasserIn) , Teutsch, Jason (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: January 8, 2014
In: Transactions of the American Mathematical Society
Year: 2014, Jahrgang: 366, Heft: 6, Pages: 3027-3041
ISSN:1088-6850
DOI:10.1090/S0002-9947-2014-05912-6
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1090/S0002-9947-2014-05912-6
Verlag, lizenzpflichtig, Volltext: https://www.ams.org/tran/2014-366-06/S0002-9947-2014-05912-6/
Volltext
Verfasserangaben:Randall Dougherty, Jack Lutz, R. Daniel Mauldin, and Jason Teutsch
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Zusammenfassung:We determine the constructive dimension of points in random translates of the Cantor set. The Cantor set ``cancels randomness'' in the sense that some of its members, when added to Martin-Löf random reals, identify a point with lower constructive dimension than the random itself. In particular, we find the Hausdorff dimension of the set of points in a random Cantor set translate with a given constructive dimension.
Beschreibung:Gesehen am 24.08.2020
Beschreibung:Online Resource
ISSN:1088-6850
DOI:10.1090/S0002-9947-2014-05912-6

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