On the exact Hausdorff dimension of the set of Liouville numbers

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

Let L denote the set of Liouville numbers. For a dimension function h, we write H-h(L) for the h-dimensional Hausdorff measure of L. In this paper we locate the exact "cut-point" at which the Hausdorff measure of L drops from infinity to zero. Namely, if h is a dimension function that increases faster than any power function near 0, then H-h(L) = infinity, and if h is a dimension function that increases slower than some power function near 0, then H-h(L) = 0. This answers a question asked by R. D. Mauldin.

Original languageEnglish
Pages (from-to)157-172
Number of pages16
JournalManuscripta Mathematica
Volume116
DOIs
Publication statusPublished - Feb 2005

Fingerprint

Dive into the research topics of 'On the exact Hausdorff dimension of the set of Liouville numbers'. Together they form a unique fingerprint.

Cite this