On strong tractability of weighted multivariate integration

We prove that for every dimension s and every number n of points, there exists a point-set Pn,s whose -weighted unanchored L∞ discrepancy is bounded from above by C(b)/n1/2−b independently of s provided that the sequence = {γk} has ∑∞ k=1 γ a k < ∞ for some (even arbitrarily large) a. Here b is a positive number that could be chosen arbitrarily close to zero and C(b) depends on b but not on s or n. This result yields strong tractability of the corresponding integration problems including approximation of weighted integrals ∫ D f(x) ρ(x) dx over unbounded domains such as D = R s. It also supplements the results that provide an upper bound of the form C √ s/n when γk ≡ 1.