Martingale Differences and the Metric Theory of Continued Fractions
نویسندگان
چکیده
Abstract. 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 R. F. Gundy. By applying known results for martingales we obtain corresponding metric theorems for the continued fraction expansion of almost all real numbers.
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تاریخ انتشار 2009