Sumsets contained in sets of upper Banach density 1

Melvyn B. Nathanson

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arXiv · 1708.01905

Sumsets contained in sets of upper Banach density 1

Melvyn B. Nathanson

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Abstract

Every set $A$ of positive integers with upper Banach density 1 contains an infinite sequence of pairwise disjoint subsets $(B_i)_{i=1}^{\infty}$ such that $B_i$ has upper Banach density 1 for all $i \in \mathbf{N}$ and $\sum_{i\in I} B_i \subseteq A$ for every nonempty finite set $I$ of positive integers.

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Melvyn B. Nathanson. 2017-08-06. Sumsets contained in sets of upper Banach density 1. https://arxiv.org/abs/1708.01905

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