AN INVERSE THEOREM: WHEN THE MEASURE OF THE SUMSET IS THE SUM OF THE MEASURES IN A LOCALLY COMPACT ABELIAN GROUP

作者：Griesmer John T^*

来源：Transactions of the American Mathematical Society, 2014, 366(4): 1797-1827.

We classify the pairs of subsets A, B of a locally compact abelian group G satisfying m(*)(A + B) = m(A) + m(B), where m is the Haar measure for G and m(*) is inner Haar measure. This generalizes M. Kneser%26apos;s classification of such pairs when G is assumed to be connected. Recently, D. Grynkiewicz classified the pairs of sets A, B satisfying vertical bar A + B vertical bar = vertical bar A vertical bar + vertical bar B vertical bar in an abelian group, and our result is complementary to that classification. Our proofs combine arguments of Kneser and Grynkiewicz.

• 出版日期2014-4