Millimetric properties of IRAS galaxies — III. Luminosity functions, sub-mm counts and contributions to the sky background

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.