%0 Journal Article
%T Some metrical results on the approximation by continued fractions
%A Hendrik Jager
%J Uniform Distribution Theory
%D 2011
%I Mathematical Institute of the Slovak Academy of Sciences
%X Let $x$ be a real irrational number and $p_n/q_n, n=1,2,\ldots$ its sequence of continued fraction convergents. Define $d_n=q_{n+1}|q_nx-p_n|.$ For almost all $x$ the distribution functions of the sequences $|d_n-d_{n+1}|$ and $d_n+d_{n+1}$ are determined.
%K Continued fraction
%K convergent
%K distribution function
%U http://www.boku.ac.at/MATH/udt/vol06/no2/10Jager11-2.pdf