  We consider a generalisation of the baker's transformation, consisting of a
skew-product of contractions and a $\beta$-transformation. The Hausdorff
dimension and Lebesgue measure of the attractor is calculated for a set of
parameters with positive measure. The proofs use a new transverality lemma
similar to Solomyak's [Solomyak, 1995]. This transversality, which is
applicable to the considered class of maps holds for a larger set of parameters
than Solomyak's transversality.
