We investigate a collection of orthonormal functions that encodes informationabout the continued fraction expansion of real numbers. When suitably orderedthese functions form a complete system of martingale differences and are aspecial case of a class of martingale differences considered by R. F. Gundy. Byapplying known results for martingales we obtain corresponding metric theoremsfor the continued fraction expansion of almost all real numbers.
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机译：我们研究了正交函数的集合，该函数对有关实数的连续分数扩展的信息进行编码。当适当地排序时，这些函数形成a差异的完整系统，并且是R. F. Gundy考虑的一类differences差异的特殊情况。通过将已知结果应用于mar，我们获得了几乎所有实数的连续分数展开的相应度量定理。
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