  We measure the z=0 B-band optical luminosity function (LF) for galaxies
selected in a blind HI survey. The total LF of the HI selected sample is flat,
with Schechter parameters M*=-19.38_{-0.62}^{+1.02} + 5 log h mag and
alpha=-1.03_{-0.15}^{+0.25}, in good agreement with LFs of optically selected
late-type galaxies. Bivariate distribution functions of several galaxy
parameters show that the HI density in the local Universe is more widely spread
over galaxies of different size, central surface brightness, and luminosity
than is the optical luminosity density. The number density of very low surface
brightness (>24.0 mag/arcsec^2) gas-rich galaxies is considerably lower than
that found in optical surveys designed to detect dim galaxies. This suggests
that only a part of the population of LSB galaxies is gas rich and that the
rest must be gas poor. However, we show that this gas-poor population must be
cosmologically insignificant in baryon content. The contribution of gas-rich
LSB galaxies (>23.0 mag/arcsec^2) to the local cosmological gas and luminosity
density is modest (18_{-5}^{+6} and 5_{-2}^{+2} per cent respectively); their
contribution to Omega_matter is not well-determined, but probably < 11 per
cent. These values are in excellent agreement with the low redshift results
from the Hubble Deep Field.
