The sumset phenomenon

DOI10.1090/S0002-9939-01-06088-9zbMath0985.03066MaRDI QIDQ2759038

Renling Jin

Publication date: 10 December 2001

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

zbMATH Keywords

nonstandard analysisLebesgue measuresyndetic

Mathematics Subject Classification ID

Density, gaps, topology (11B05) Additive bases, including sumsets (11B13) Nonstandard models of arithmetic (03H15) Nonstandard models in mathematics (03H05) Nonstandard measure theory (28E05)

Related Items (23)

A monad measure space for logarithmic density ⋮ Multiplicative structures in additively large sets ⋮ Sumset phenomenon in locally compact topological groups ⋮ Ramsey properties of nonlinear Diophantine equations ⋮ An elementary proof of Jin's theorem with a bound ⋮ Subsets of virtually nilpotent groups with the SBM property ⋮ Small-sum pairs for upper Banach density in countable abelian groups ⋮ HIGH DENSITY PIECEWISE SYNDETICITY OF PRODUCT SETS IN AMENABLE GROUPS ⋮ On Supra-SIM Sets of Natural Numbers ⋮ Inverse problem for cuts ⋮ An ultrafilter approach to Jin's theorem ⋮ Sumsets of dense sets and sparse sets ⋮ Product set phenomena for countable groups ⋮ A combinatorial proof of the dense Hindman's theorem ⋮ Dichotomy and infinite combinatorics: the theorems of Steinhaus and Ostrowski ⋮ Product set phenomena for measured groups ⋮ Near arithmetic progressions in sparse sets ⋮ WM groups and Ramsey theory ⋮ Sumset phenomenon in countable amenable groups ⋮ Nonstandard analysis and the sumset phenomenon in arbitrary amenable groups ⋮ High density piecewise syndeticity of sumsets ⋮ Intersections of shifted sets ⋮ Abelian groups with layered tiles and the sumset phenomenon

Cites Work

• Nonstandard methods for upper Banach density problems.
• Meager sets on the hyperfinite time line
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