# 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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