Before revision:  We obtain these results under the same moment restrictions and conditions on the class of functions as with i.i.d. data. As a result, convergence and asymptotic normality of nonlinear estimators can be obtained under the same regularity conditions as with i.i.d. data.
After revision:  We obtain these results under the same moment restrictions and conditions on the class of functions as those typically assumed with i.i.d. data.