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

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JournalAnnals of Mathematics
DatePublished - Nov 2006
Issue number3
Volume164
Number of pages21
Pages (from-to)971-992
Original languageEnglish

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.

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