A statistical approach to covering lemmas

We discuss a statistical variant of Ruzsa’s covering lemma and use it to show that if GG is an Abelian group of bounded exponent and A⊂GA⊂G has |A+A|⩽K|A||A+A|⩽K|A| then the subgroup generated by AA has size at most exp(O(Klog22K))|A|exp(O(Klog22K))|A|, where the constant in the big-OO depends on the exponent of the group only.