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

Let A and B be two infinite sets of non-negative integers. Similar to Kneser's Theorem (Theorem 1.1 below) we characterize the structure of A + B when the upper Banach density of A + B is less than the sum of the upper Banach density of A and the upper Banach density of B.

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Bibliographic Details
Published inJournal of number theory Vol. 130; no. 8; pp. 1785 - 1800
Main Author Jin, Renling
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2010
Subjects
Kneser's Theorem
Lower asymptotic density
Nonstandard analysis
Upper Banach density
Lower asymptotic density
03H15
Nonstandard analysis
Upper Banach density
11B13
11B05
11U10
Kneser's Theorem
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Summary:Let A and B be two infinite sets of non-negative integers. Similar to Kneser's Theorem (Theorem 1.1 below) we characterize the structure of A + B when the upper Banach density of A + B is less than the sum of the upper Banach density of A and the upper Banach density of B.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2010.02.008