  The HI mass function (HIMF) for galaxies in the local universe is constructed
from the results of the Arecibo HI Strip Survey, a blind extragalactic survey
in the 21cm line. The survey consists of two strips covering in total 65 square
degrees of sky, with a depth of cz = 7400 km/s and was optimized to detect
column densities of neutral gas N_HI > 10^18 cm^-2 (5 sigma). The survey
yielded 66 significant extragalactic signals of which approximately 50% are
cataloged galaxies. No free floating HI clouds without stars are found. VLA
follow-up observations of all signals have been used to obtain better
measurements of the positions and fluxes and allow an alternate determination
of the achieved survey sensitivity. The resulting HIMF has a shallow faint end
slope (alpha ~ 1.2), and is consistent with earlier estimates computed for the
population of optically selected gas rich galaxies. This implies that there is
not a large population of gas rich low luminosity or low surface brightness
galaxies that has gone unnoticed by optical surveys. The cosmological mass
density of HI at the present time determined from the survey, Omega_HI = (2.0
+/- 0.5) x 10^-4, is in good agreement with earlier estimates. We determine
lower limits to the average column densities <N_HI> of the galaxies detected in
the survey and find that none of the galaxies have <N_HI> below 10^19.7 cm^-2,
although there are no observational selection criteria against finding lower
density systems.
