Abstract
Here we consider integration methods with error bounded below by $$mn^{-\alpha }$$mn-? for a constant $$m>0$$m>0 and rate $$\alpha >1$$?>1. Suppose that simple averages along an extensible sequence have error at most $$Mn^{-\alpha }$$Mn-? for all $$n$$n in an infinite sequence of sample sizes $$n_1
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