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The Universidad Complutense de Madrid (UCM) Survey is a long-term projectaiming at finding and analysing star-forming galaxies detected by theirH$\alpha$ emission in Schmidt objective-prism plates. The instrumental set-uplimits the volume of the Universe surveyed to a redshift $z\lesssim0.045$. Sofar we have discovered several hundred emission-line galaxies (ELGs) undergoingstar formation at a wide range of levels. Analyzing a complete sample of ELGsfrom the UCM survey we have computed the H$\alpha$ luminosity function for thestar-forming galaxies in the surveyed volume of the Universe. A Schechterfunction provides a good fit to the H$\alpha$ luminosity function with thefollowing parameters: $\alpha = -1.3\pm0.2$; $L^*({\rm H}\alpha) =10^{42.15\pm0.08} $erg$ $s$^{-1}$ and $\phi^*=10^{-3.2\pm0.2} $Mpc$^{-3}$ for$H_0 = 50 $km$ $s$^{-1} $Mpc$^{-1}$. Integrating over the full range ofluminosities, we obtain an H$\alpha$ luminosity density of $10^{39.1\pm0.2}$erg$ $s$^{-1} $Mpc$^{-3}$. Using the H$\alpha$ emission as a star formationrate (SFR) estimator, this translates into a SFR density for the Local Universeof $0.013^{+0.007}_{-0.005} M_{\odot} $yr$^{-1} $Mpc$^{-3}$ in star-forminggalaxies with $EW($H$\alpha+$[NII]$)>10$\AA and $z\lesssim0.045$, for a ScaloInitial Mass Function. This is the first observational determination of thisquantity, which will provide a direct test of current galaxy formation andevolution models.Comment: 16 pages, PS file, 1 table and 1 figure. Accepted in ApJ

Erratum: “The Current Star Formation Rate of the Local Universe” (ApJ, 455, L1 [1995])