a1 School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW. e-mail: Thomas.Jordan@bristol.ac.uk
a2 Department of Mathematics, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, GU2 7XH, UK. e-mail: firstname.lastname@example.org
a3 Department of Mathematics, University of Washington, Box 354 350, Seattle WA 98195-5350, U.S.A. e-mail: email@example.com
Let νpλ be the distribution of the random series , where in is a sequence of i.i.d. random variables taking the values 0, 1 with probabilities p, 1 − p. These measures are the well-known (biased) Bernoulli convolutions.
In this paper we study the multifractal spectrum of νpλ for typical λ. Namely, we investigate the size of the sets
(Received November 09 2010)
(Online publication August 19 2011)
† Supported by EPSRC grant EP/E050441/1 and the University of Manchester.
‡ Supported in part by NSF grants DMS-0654408 and DMS-0968879.