ABSTRACT
The aim of this part is to modify the usual simple continued fraction by considering another one whose numerators are always equal to a positive constant a. The authors study the convergence of this new type of continued fraction and prove that it is generated by a mapping Ta which is measure-preserving and ergodic with respect to some measure µa on the Borel subsets of [0, 1]. The latter is then applied to extend several theorems going back to Khintchine and Levy to the case of a-simple continued fractions.
