  We perform a measurement of the tau -> l gamma nu anti-nu (l = e, mu)
branching fractions for a minimum photon energy of 10 MeV in the tau rest
frame, using 431fb^-1 of e^+e^- collisions collected at the center-of-mass
energy of the Upsilon(4S) resonance with the BaBar detector at the PEP-II
storage rings. We find B(tau -> mu gamma nu anti-nu ) =
(3.69pm0.03pm0.10)x10^-3, and B(tau -> e gamma nu anti-nu ) =
(1.847pm0.015pm0.052)x10^-2, where the first quoted error is statistical, and
the second is systematic. These results are substantially more precise than
previous measurements.
