Abstract
In this paper, we show the existence of the Lelong-Demailly numbers of positive S-plurisubharmonic currents. Moreover, a valid definition of dd(c)g boolean AND T is obtained for plurisubharmonic currents T and unbounded plurisubharmonic functions g. The importance of this definition comes from the sharpness of our condition on the Hausdorff dimension of the locus points of g.