Hausdorff dimensions in Pierce expansions

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

References in corpus (1)

• On the error-sum function of Pierce expansions

Cited by in corpus (4)

• Exceptional sets to Shallit's law of leap years in Pierce expansions
• Convergence exponent of Pierce expansion digit sequences
• Representations of Real Numbers by Alternating Perron Series and Their Geometry
• An elementary proof that the set of exceptions to the law of large numbers in Pierce expansions has full Hausdorff dimension