A Freiman-type theorem for locally compact abelian groups

Abstract

We prove a Freiman-type theorem for locally compact abelian groups. If A is a subset of a locally compact abelian group with Haar measure m and m(nA) < n^dm(A) for all n>d log d then we describe A in a way which is tight up to logarithmic factors in d.

12 pp. Corrected typos. Updated references. Minor revisions.