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

@article{Beresnevich2004AMT,
  title={A mass transference principle and the Duffin-Schaeffer conjecture for Hausdorff measures},
  author={Victor Beresnevich and Sanju Velani},
  journal={Annals of Mathematics},
  year={2004},
  volume={164},
  pages={971-992}
}
A Hausdorff measure version of the Duffin-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 lim sup subsets of R k to Hausdorff measure theoretic statements. In view of this, the Lebesgue theory of lim sup sets is shown to underpin the general Hausdorff theory. This is rather surprising… 

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