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Published: 2009

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This thesis presents an analysis of inclusive semileptonic $B \to X_u e \nu$ decays using approximately 454 million $\Upsilon(4S) \to B \bar{B}$ decays collected during the years 1999 to 2008 with the BABAR detector. The electron energy, $E_e$, and the invariant mass squared of the electron-neutrino pair, $ q^2$, are reconstructed, where the neutrino kinematics is deduced from the decay products of both B mesons. The final hadronic state, $ X_u$, consists of a sum of many hadronic channels, each of which contains at least one $u$ quark. The variables $q^2$ and $E_e$ are then combined to compute the maximum kinematically allowed invariant mass squared of the hadronic system, $s_h^{max}$. Using these kinematic quantities, the partial branching fraction, $\Delta BR(B \to X_u e \nu)$, unfolded for detector effects, is measured to be $\Delta BR(E_e>2.0 GeV, s_h^{max}3.52 GeV^2) = (3.33 \pm 0.18 \pm 0.21) \times 10^{-4} in the $\Upsilon(4S)$ and \Delta \tilde{\BR}(\tilde E_e1.9 GeV, \tilde {s}^{max}_{h}