On the maximal density of sum-free sets

  title={On the maximal density of sum-free sets},
  author={Tomasz Luczak and Tomasz Schoen},
Theorem 1 is due to Folkman [4], who also asked whether its assertion remains true if ε > 0 is replaced by a function which tends to 0 as n →∞. Theorem 2 below states that this is indeed the case and, furthermore, for every set A dense enough, one can take b = 0. It should be mentioned that recently a similar result has been independently proved by Hegyvári [5], who showed that the assertion of Theorem 1 holds for all A ⊆ N with A(n) > 300 √ n log n for n large enough.