We investigate a collection of orthonormal functions that encodes information about the continued fraction expansion of real numbers. When suitably ordered these functions form a complete system of martingale differences and are a special case of a class of martingale differences considered by Gundy. By applying known results for martingales, we obtain corresponding metric theorems for the continued fraction expansion of almost all real numbers.
|Translated title of the contribution||Martingale differences and the metric theory of continued fractions|
|Pages (from-to)||213 - 242|
|Number of pages||30|
|Journal||Illinois Journal of Mathematics|
|Volume||52, number 1|
|Publication status||Published - Mar 2008|