An inverse theorem: when m(A+B)=m(A)+m(B) in a locally compact abelian group

Details An inverse theorem: when m(A+B)=m(A)+m(B) in a locally compact abelian group An inverse theorem: when m(A+B)=m(A)+m(B) in a locally compact abelian group

2011-12-29

arxiv.org/abs/1112.6403v1

Mathematics

Combinatorics

27 pages, 1 figure

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

An inverse theorem: when m(A+B)=m(A)+m(B) in a locally compact abelian group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An inverse theorem: when m(A+B)=m(A)+m(B) in a locally compact abelian group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An inverse theorem: when m(A+B)=m(A)+m(B) in a locally compact abelian group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-334188