An inverse theorem: When the measure of the sumset is the sum of the measures in a locally compact abelian group

DOI10.1090/S0002-9947-2013-06022-9zbMath1300.11102arXiv1112.6403OpenAlexW2101123180MaRDI QIDQ5401743

John T. Griesmer

Publication date: 12 March 2014

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

Full work available at URL: https://arxiv.org/abs/1112.6403

zbMATH Keywords

Haar measuresumsetlocally compact abelian groupcritical pair

Mathematics Subject Classification ID

Finite abelian groups (20K01) Additive bases, including sumsets (11B13) Set functions and measures on topological groups or semigroups, Haar measures, invariant measures (28C10) Inverse problems of additive number theory, including sumsets (11P70)

Related Items

Semicontinuity of structure for small sumsets in compact abelian groups, Inequalities of Riesz-Sobolev type for compact connected abelian groups, An inverse theorem for an inequality of Kneser

Cites Work

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• Summenmengen in lokalkompakten abelschen Gruppen
• Eine Verschärfung für Abschätzungen von Summenmengen in lokalkompakten Gruppen
• Characterizing the structure of \(A+B\) when \(A+B\) has small upper Banach density
• On small sumsets in an abelian group
• Quasi-periodic decompositions and the Kemperman structure theorem
• The Critical Pairs of Subsets of a Group of Prime Order
• A Step Beyond Kemperman's Structure Theorem
• An inverse theorem mod p
• The (α+2β)-Inequality on a Torus
• On products of sets in a locally compact group
• On the critical pair theory in Z/pZ
• Three Results for Locally Compact Groups Connected with the Haar Measure Density Theorem
• On the Measure of Sum-Sets. (I) The Theorems of Brunn, Minkowski, and Lusternik
• Sur la mesure d'une somme vectorielle