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A mass transference principle and the Duffin-Schaeffer conjecture for Hausdorff measures

Beresnevich, V. and Velani, S. (2006) A mass transference principle and the Duffin-Schaeffer conjecture for Hausdorff measures. Annals of Mathematics, 164 (3). pp. 971-992. ISSN 0003-486X

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Abstract

A Hausdorff measure version of the Dufin-Schaeffer conjecture in metric number theory is introduced and discussed. The general conjecture is established modulo the original conjecture. The key result is a Mass Transference Principle which allows us to transfer Lebesgue measure theoretic statements for limsup subsets of Rk to Hausdorff measure theoretic statements. In view of this, the Lebesgue theory of limsup sets is shown to underpin the general Hausdorff theory. This is rather surprising since the latter theory is viewed to be a subtle refinement of the former.

Item Type: Article
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 21 Aug 2009 14:50
Last Modified: 21 Aug 2009 14:50
Published Version: http://annals.princeton.edu/annals/2006/164-3/p06....
Status: Published
Publisher: Princeton University
URI: http://eprints.whiterose.ac.uk/id/eprint/5585

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