  We exploit observations at 1.25 mm with the ESO-SEST telescope of a southern
galaxy sample, selected from the IRAS PSC and complete to $S_{60}=2 Jy$, to
derive the FIR and mm luminosity functions and the conditional probability
distributions of FIR and mm luminosity of galaxies. The reliability of these
estimates is ensured by the good observed correlation of the far-infrared and
mm emissions. This detailed knowledge of the millimetric properties of galaxies
is used to simulate the extragalactic sub-mm sky (background intensity,
small-scale anisotropy signals, and discrete source statistics) -- that will be
investigated soon by a variety of ground-based and space observatories. We
find, in particular, that the recent tentative detection of a sub-mm background
would require, if confirmed, strong evolution with cosmic time of the galaxy
long-wavelength emissivity. We finally emphasize the difficulty to test such
evolution through observations from currently available millimetric sites on
ground.
