The Duffin-Schaeffer Conjecture with extra divergence II
  This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true. 
Victor Beresnevich, Glyn Harman, Alan Haynes and Sanju Velani
math.NT