Intersections of sumsets in additive number theory

Abstract: Let $A$ be a subset of an additive abelian semigroup and let $hA$ be the $h$-fold sumset of $A$. The following question is considered: Let $(A_q){q=1}^{\infty}$ be a strictly decreasing sequence of sets in the semigroup and let $A = \bigcap{q=1}^{\infty} A_q$. When does one have [ hA = \bigcap_{q=1}^{\infty} hA_q ] for some or all $h \geq 2$?