A proof of Niederreiter's conjecture concerning error bounds for quasi-Monte Carlo integration

In this paper Niederreiter's error bound for quasi-Monte Carlo integration on bounded Jordan measurable subsets of the k-dimensional unit cube E^k is improved. The new error bound, which has been conjectured by Niederreiter, reduces to the corresponding error bound given by Zaremba in case of integration on convex subsets of E^k.