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

2011/12/29 by John T. Griesmer, Griesmer, John T.
Mathematics · #11P70 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1112.6403

openalex publication_date 2011/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the pairs of subsets (A,B) of a locally compact abelian group\nsatisfying m(A+B)=m(A)+m(B), where m is Haar measure. This generalizes a result\nof M. Kneser classifying such pairs under the additional assumption that G is\ncompact and connected. Our proof combines Kneser's proof with arguments of D.\nGrynkiewicz, who classified the pairs of subsets (A,B) of abelian groups\nsatisfying |A+B|=|A|+|B|, where |A| is the cardinality of A.\n

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