Kneser's Theorem (Combinatorics)

Kneser's theorem, in additive combinatorics, refers to a group of related results about the size of sumsets in abelian groups, published by Martin Kneser in 1953 and 1956. The theorems extend the Cauchy-Davenport theorem, which bounds sumset sizes only for groups of prime order, to general abelian groups, with several statements addressing when a sumset stays strictly smaller than the sum of the sizes of its two component sets, and a further statement addressing when equality holds for Haar measure in connected compact abelian groups.