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: | , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
January 8, 2014
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| 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/ 
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| Verfasserangaben: | Randall Dougherty, Jack Lutz, R. Daniel Mauldin, and Jason Teutsch |
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| 520 | |a 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. | ||
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