A FREIMAN-TYPE THEOREM FOR LOCALLY COMPACT ABELIAN GROUPS

摘要

Suppose that G is a locally compact abelian group with a Haar measure mu. The delta-ball B-delta of a continuous translation invariant pseudo-metric is called d-dimensional if mu(B-2 delta') = d log d, then A is contained in an O(d log(3) d)-dimensional ball, B, of positive radius in some continuous translation invariant pseudo-metric and 1(B) exp(O(d log d))mu(A).