We present results of the first unbiased search for extended UV (XUV)-disk galaxies undertaken to determine the space density of such galaxies. Our sample contains 561 local (0.001 < z < 0.05) galaxies that lie in the intersection of available GALEX deep imaging (exposure time > 1.5 x 10^4 s) and SDSS DR7 footprints. We explore modifications to the standard classification scheme for our sample that includes both disk- and bulge-dominated galaxies. Visual classification of each galaxy in the sample reveals an XUV-disk frequency of up to 20% for the most nearby portion of our sample. On average over the entire sample (out to z=0.05) the frequency ranges from a hard limit of 4% to 14%. The GALEX imaging allows us to detect XUV-disks beyond 100 Mpc. The XUV regions around XUV-disk galaxies are consistently bluer than the main bodies. We find a surprisingly high frequency of XUV emission around luminous red (NUV-r > 5) and green valley (3 < NUV-r < 5) galaxies. The XUV-disk space density in the local universe is > 1.5-4.2 x 10^-3 Mpc^-3. Using the XUV emission as an indicator of recent gas accretion, we estimate that the cold gas accretion rate onto these galaxies is > 1.7-4.6 x 10^-3 Msun Mpc^-3 yr^-1. The number of XUV-disks in the green valley and the estimated accretion rate onto such galaxies points to the intriguing possibility that 7%-18% of galaxies in this population are transitioning away from the red sequence.
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