Translating the Cantor set by a random real-Reference-Cited by-同舟云学术

Translating the Cantor set by a random real

Published:2014-01-08 Issue:6 Volume:366 Page:3027-3041
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Dougherty Randall,Lutz Jack,Mauldin R. Daniel,Teutsch Jason

Abstract

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2014-366-06/S0002-9947-2014-05912-6/S0002-9947-2014-05912-6.pdf

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