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

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.