Research output: Contribution to journal › Article

Journal | Annals of Mathematics |
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Date | Published - Nov 2006 |

Issue number | 3 |

Volume | 164 |

Number of pages | 21 |

Pages (from-to) | 971-992 |

Original language | English |

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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