A GENERALIZED DISCREPANCY AND QUADRATURE ERROR BOUND

An error bound for multidimensional quadrature is derived that include s the Koksma-Hlawka inequality as a special case. This error bound tak es the form of a product of two terms. One term, which depends only on the integrand, is defined as a generalized variation. The other term, which depends only on the quadrature rule, is defined as a generalize d discrepancy. The generalized discrepancy is a figure of merit for qu adrature rules and includes as special cases the L-p-star discrepancy and P-alpha that arises in the study of lattice rules.