For the Gauss map frac, we can fairly easily show that it preserves the Gauss measure by considering the so-called basic sets for . The pre-image of the set is the set of intervals for . The measures of these intervals add up toOther sets in may be formed by countable unions and intersections of these sets, and hence the Gauss measure is preserved by the Gauss map. The only difficult part of this computation is the evaluation of the sum in the middle, and this is tedious but straightforward. In passing I note that Maple can evaluate this sum, when properly coached.