  The weighted star-discrepancy has been introduced by Sloan and
Wo{\'z}niakowski to reflect the fact that in multidimensional integration
problems some coordinates of a function may be more important than others. It
provides upper bounds for the error of multidimensional numerical integration
algorithms for functions belonging to weighted function spaces of Sobolev type.
In the present paper, we prove several tractability results for the weighted
star-discrepancy. In particular, we obtain rather sharp sufficient conditions
under which the weighted star-discrepancy is strongly tractable. The proofs are
probabilistic, and use empirical process theory.
