New York Journal of Mathematics
Volume 19 (2013) 285-303


K. Dajani and C. Kalle

Local dimensions for the random β-transformation

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Published: June 7, 2013
Keywords: β-expansion, random transformation, Bernoulli convolution, local dimension, Pisot number
Subject: Primary, 37A05, 37C45, 11K16, 42A85.

The random β-transformation K is isomorphic to a full shift. This relation gives an invariant measure for K that yields the Bernoulli convolution by projection. We study the local dimension of the invariant measure for K for special values of β and use the projection to obtain results on the local dimension of the Bernoulli convolution.


The second author was supported by NWO (Veni grant no. 639.031.140).

Author information

K. Dajani:
Department of Mathematics, Utrecht University, Postbus 80.000, 3508 TA Utrecht, the Netherlands

C. Kalle:
Mathematical Institute, Leiden University, Postbus 9512, 2300 RA Leiden, the Netherlands