Weighted integration over a hyperrectangle based on digital nets and sequences

Quasi-Monte Carlo (QMC) methods are equal weight quadrature rules to approximate integrals over the unit cube with respect uniform measure. In this paper we discuss QMC integration general product measures defined on an arbitrary hyperrectangle. We only require that cumulative distribution function is invertible. develop a worst-case error bound and study dependence of number points dimension for digital nets sequences as well polynomial lattice point sets, which mapped domain using inverse function. do not any smoothness properties probability density does depend particular choice its smoothness. The component-by-component construction based criterion depends size hyperrectangle but otherwise independent