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تسجيل مستخدم جديدA natural probability measure derived from Sterns diatomic sequence
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Sterns diatomic sequence with its intrinsic repetition and refinement structure between consecutive powers of $2$ gives rise to a rather natural probability measure on the unit interval. We construct this measure and show that it is purely singular continuous, with a strictly increasing, Holder continuous distribution function. Moreover, we relate this function with the solution of the dilation equation for Sterns diatomic sequence.
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