Characterizing the structure of \(A+B\) when \(A+B\) has small upper Banach density

DOI10.1016/j.jnt.2010.02.008zbMath1201.11016OpenAlexW2025095324MaRDI QIDQ982530

Renling Jin

Publication date: 7 July 2010

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2010.02.008

zbMATH Keywords

upper Banach densitysum sets

Mathematics Subject Classification ID

Density, gaps, topology (11B05) Additive bases, including sumsets (11B13)

Related Items (4)

Approximate invariance for ergodic actions of amenable groups ⋮ Semicontinuity of structure for small sumsets in compact abelian groups ⋮ Small-sum pairs for upper Banach density in countable abelian groups ⋮ An inverse theorem: When the measure of the sumset is the sum of the measures in a locally compact abelian group

Cites Work

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• Kneser's theorem for upper Banach density
• Addition of sets of integers of positive density
• Nonstandard methods for upper Banach density problems.
• Freiman's inverse problem with small doubling property
• Solution to the inverse problem for upper asymptotic density

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