A short proof of a conjecture of Erd\"os proved by Moreira, Richter and Robertson
Bernard Host

TL;DR
This paper provides a concise proof of Erd"os's sumset conjecture, demonstrating that any positive density subset of integers contains the sum of two infinite sets, using classical ergodic theory.
Contribution
It offers a shorter, ergodic theory-based proof of a recent result by Moreira, Richter, and Robertson on sumsets in positive density subsets.
Findings
Confirmed that positive density subsets contain sum of two infinite sets
Provided a more concise proof using ergodic theory
Strengthened understanding of sumset structure in integers
Abstract
We give a short proof of a sumset conjecture of Erd\"os, recently proved by Moreira, Richter and Robertson: every subset of the integers of positive density contains the sum of two infinite sets. The proof is written in the framework of classical ergodic theory.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Mathematical Dynamics and Fractals
