  In an earlier work, joint with R. Kenyon, we computed the Hausdorff dimension
of the "multiplicative golden mean shift" defined as the set of all reals in
[0,1] whose binary expansion (x_k) satisfies x_k x_{2k}=0 for all k=1,2... Here
we show that this set has infinite Hausdorff measure in its dimension. A more
precise result in terms of gauges in which the Hausdorff measure is infinite is
also obtained.

Dynamical Systems