Plünnecke’s Theorem for asymptotic densities

DOI10.1090/S0002-9947-2011-05533-9zbMath1277.11006MaRDI QIDQ3093462

Renling Jin

Publication date: 17 October 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

nonstandard analysisbasisPlünnecke's inequalityupper Banach densityupper asymptotic densitylower asymptotic densityShnirel'man density

Mathematics Subject Classification ID

Density, gaps, topology (11B05) Additive bases, including sumsets (11B13) Nonstandard models of arithmetic (03H15) Nonstandard arithmetic (number-theoretic aspects) (11U10)

Related Items (5)

Multidimensional lower density versions of Plünnecke's inequality ⋮ Plünnecke inequalities for countable abelian groups ⋮ Plünnecke inequalities for measure graphs with applications ⋮ A compendium of results in additive number theory ⋮ Intersections of shifted sets

Cites Work

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• Über die schwache Basisordnung
• Kneser's theorem for upper Banach density
• A note on uniform or Banach 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
• Eine zahlentheoretische Anwendung der Graphentheorie.
• On Goldbach's Problem : Proof that Almost all Even Positive Integers are Sums of Two Primes
• On Waring's problem for cubes

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