Hausdorff dimensions in Pierce expansions
arXiv:2304.14162 · doi:10.4064/aa230427-18-3
Abstract
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 Hausdorff dimensions of the exceptional sets of each of the three laws. We further determine the Hausdorff dimensions of certain sets arising in Pierce expansions.
46 pages; proof of Lemma 4.6 revised; typos corrected