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{{harvtxt|Duffin|Schaeffer|1941}} proved a generalization of Khinchin's result, and posed what is now known as the [[Duffin–Schaeffer conjecture]] on the analogue of Khinchin's dichotomy for general, not necessarily decreasing, sequences <math>\psi</math> . {{harvtxt|Beresnevich|Velani|2006}} proved that a [[Hausdorff measure]] analogue of the Duffin–Schaeffer conjecture is equivalent to the original Duffin–Schaeffer conjecture, which is a priori weaker.
In July 2019, Dimitris Koukoulopoulos and [[James Maynard (mathematician)|James Maynard]] announced a proof of the conjecture.<ref>{{cite arXiv |first1=D. |last1=Koukoulopoulos |first2=J. |last2=Maynard |title=On the Duffin–Schaeffer conjecture |year=2019 |
=== Hausdorff dimension of exceptional sets ===
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