We present measurements of the inclusive production of antideuterons in annihilation into hadrons at $\approx 10.58 \mathrm{,Ge\kern -0.1em V}\Upsilon(1S,2S,3S)$ decays. The results are obtained using data collected by the BABAR detector at the PEP-II electron-positron collider. Assuming a fireball spectral shape for the emitted antideuteron momentum, we find $(\Upsilon(1S) \to \bar{d}X) = (2.81 \pm 0.49 {}^{+0.20}{-0.24} )/! \times /! 10^{-5}(\Upsilon(2S) \to \bar{d}X) = (2.64 \pm 0.11 {}^{+0.26}{-0.21} )/! \times /! 10^{-5}(\Upsilon(3S) \to \bar{d}X) = (2.33 \pm 0.15 {}^{+0.31}{-0.28} )/! \times /! 10^{-5}\sigma (e^+e^- \to \bar{d}X) = (9.63 \pm 0.41 {}^{+1.17}{-1.01} ) \mbox{,fb}$.

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