  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.
