Gauss map vs Bernoulli shift

Abstract: This paper shows that blocks of different entries and different lengths can have the same probability of occurrence in the representation of any continued fraction which its orbit distributed according to Gauss measure. More precisely there are blocks of even lengths and 3-blocks which their probability of occurrence equals to the probability of occurrence of a unit block, and this property is not satisfied by the Bernoulli shift. [Copyright &y& Elsevier]