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math.NT2024
An elementary proof that the set of exceptions to the law of large numbers in Pierce expansions has full Hausdorff dimension
Min Woong Ahn
The digits of the Pierce expansion satisfy the law of large numbers. It is known that the Hausdorff dimension of the set of exceptions to the law of large numbers is 1. We provide…
math.NT2023★ 8 cited
Hausdorff dimensions in Pierce expansions
Min Woong Ahn
The digits of Pierce expansion obey the law of large numbers, the central limit theorem, and the law of the iterated logarithm in the Lebesgue measure sense. We calculate the Hausd…