J. Number Theory
- J. Number Theory
Thus ergodic theory yields a statement concerning the distribution of digits in the expansion of almost all x. Much information of a similar character can be derived. This paper is an attempt to utilize these ergodic theory results to deduce related results concerning the rationals, a set of Lebesgue measure zero. Our results are known for one-dimensional continued fractions [S, p. 3281 but do not appear to have been deduced for the general case. In this connection, see  for a computational treatment of oneand two-dimensional continued fractions.