A statistical approach to covering lemmas

We discuss a statistical variant of Ruzsa's covering lemma and use it to show that if G is an Abelian group of bounded exponent and A subset of G has vertical bar A + A vertical bar <= K vertical bar A vertical bar then the subgroup generated by A has size at most exp(O(K log(2) 2K))vertical bar A vertical bar, where the constant in the big-O depends on the exponent of the group only. (C) 2015 Published by Elsevier Ltd.