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MR2018932 (2004k:37069) 37D50 (11Z05 28A80 37A25 82C05)
Cheung, Yitwah Hausdorff dimension of the set of nonergodic directions. With an appendix by M. Boshernitzan. Ann. of Math. (2) 158 (2003), no. 2, 661--678.
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