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We report a measurement of the inclusive charmless semileptonic
branching fraction of $B$ mesons in a sample of 89 million \BB\ events
recorded with the \babar\ detector at the $\Upsilon(4S)$ resonance. Events
are selected by fully reconstructing the decay of one $B$ meson and
identifying a charged lepton from the decay of the other $B$
meson. The number of signal events is extracted from the hadronic mass
distribution and is used to determine the ratio of branching fractions
${\BR(\Bxulnu)/\BR(\Bxlnu)} = (2.06 \pm 0.25(stat)
\pm 0.23(syst) \pm 0.36(theo))\times 10^{-2}$.
Using the measured branching fraction for inclusive semileptonic $B$
decays, we find
$\BR(\Bxulnu) = (2.24 \pm 0.27(stat) \pm 0.26(syst) \pm 0.39(theo))\times 10^{-3}$
and derive the CKM matrix element
$|V_{ub}| = (4.62 \pm 0.28(stat)\pm 0.27(syst) \pm 0.48 (theo))\times 10^{-3}$.
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