A proof of a sumset conjecture of Erdos

Joel Moreira, Florian K. Richter, Donald Robertson

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


In this paper we show that every set A⊂ℕ with positive density contains B+C for some pair B,C of infinite subsets of ℕ, settling a conjecture of Erdos. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups.

Original languageEnglish (US)
Pages (from-to)605-652
Number of pages48
JournalAnnals of Mathematics
Issue number2
StatePublished - Mar 1 2019


  • Almost periodic functions
  • Sum sets
  • Ultrafilters

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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