We report a measurement of the inclusive semileptonic $B_s^0$ branching fraction in a $121~fb^{-1}$ data sample collected near the $Upsilon(5S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^+ e^-$ collider. Events containing $B_s^0$ pairs are selected by reconstructing a tag side $D_s^+$ and identifying a signal side lepton $ell^+$ ($ell = e, mu$) that is required to have the same-sign charge to ensure that both originate from different $B_s^0$ mesons. The $B_s^0 rightarrow X^- ell^+ u_ell$ branching fraction is extracted from the ratio of the measured yields of $D_s^+$ mesons and $D_s^+ ell^+$ pairs and the known production and branching fractions. The inclusive semileptonic branching fraction is measured to be $[9.6 pm 0.4text{(stat)} pm 0.7text{(syst)}]~%$.
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