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arXiv · 1112.6403

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

John T. Griesmer
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Abstract

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

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John T. Griesmer. 2013-07-27. An inverse theorem: when the measure of the sumset is the sum of the measures in a locally compact abelian group. https://arxiv.org/abs/1112.6403

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