The \ion H1 mass function ( H i MF ) for galaxies in the local universe is constructed from the results of the Arecibo \ion H1 Strip Survey , a blind extragalactic survey in the 21cm line .
The survey consists of two strips covering in total \sim 65 square degrees of sky , with a depth of cz = 7400 { km s } ^ { -1 } 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 \ion H1 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 H i MF has a shallow faint end slope ( \alpha \approx 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 influence of large scale structure on the determination of the H i MF from the Arecibo \ion H1 Strip Survey is tested by numerical experiments and was not found to affect the resulting H i MF significantly .
The cosmological mass density of \ion H1 at the present time determined from the survey , \Omega _ { HI } ( z = 0 ) = ( 2.0 \pm 0.5 ) \times 10 ^ { -4 } h ^ { -1 } , is in good agreement with earlier estimates .
We determine lower limits to the average column densities \langle N _ { HI } \rangle of the galaxies detected in the survey and find that none of the galaxies have \langle N _ { HI } \rangle < 10 ^ { 19.7 } cm ^ { -2 } , although there are no observational selection criteria against finding lower density systems .
Eight percent of the signals detected in the original survey originated in groups of galaxies , whose signals chanced to coincide in frequency .