It is well-known that many notions of geometrical discrepancy are closely related to the worst-case error of numerical multivariate integration (which we want to call "numerical discrepancy") on certain function spaces. In the case where the integrands are functions of a reproducing kernel Hilbert space a quite general relation was proved in a recent paper of Erich Novak and Henryk Wozniakowski. In Volume 2 of their new book on tractability they asked for a generalization which also covers the case of weighted reproducing kernel Hilbert spaces. In this talk we want to present their result and such a generalization.
Enquiries: Bill McLean