May 3, 2024Open Access

Hausdorff dimension of the exceptional set of the law of large numbers in Pierce expansions

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Abstract

The digits of Pierce expansion adhere to 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 offer an elementary proof of this fact by adapting Jun Wu's method used in the context of Engel expansions.

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Min Woong Ahn (Fri,) studied this question.

synapsesocial.com/papers/68e6bbccb6db64358763c494 https://doi.org/https://doi.org/10.48550/arxiv.2405.02174

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