Ricci limit spaces are semi-locally simply connected

Let (X, p) be a Ricci limit space. We show that for any 0 and x X, there exists r, depending on and x, so that any loop in Bᵣ (x) is contractible in B_ (x). In particular, X is semi-locally simply connected. Then we show that the generalized Margulis lemma holds for Ricci limit spaces of n-manifolds.