Absolutely continuous invariant measures for multidimensional expanding maps

We investigate the existence and statistical properties of absolutely conti nuous invariant measures for multidimensional expanding maps with singulari ties. The key point is the establishment of a spectral gap in the spectrum of the transfer operator. Our assumptions appear quite naturally for maps w ith singularities. We allow maps that are discontinuous on some extremely w ild sets, the shape of the discontinuities being completely ignored with ou r approach.