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Apr 17, 2014 at 12:47 comment added user25199 An explicit example of Hausdorff dimension 1/2 may be found in Y. Cheung, "Hausdorff Dimension of the Set of Nonergodic Directions", Ann Math 158, 661-678 (2003).
Apr 17, 2014 at 11:27 history answered Carlo Beenakker CC BY-SA 3.0