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We present a measurement of Z0 boson and Drell-Yan production cross sections in p̅p collisions at √s =1.8 TeV using a sample of 107 pb-1 accumulated by the Collider Detector at Fermilab. The Drell-Yan cross section is measured in the mass range of Mμμ>40 GeV/c2. We compare the measurements with the predictions of quantum chromodynamics in both leading order and next-to-leading order, incorporating the recent parton distribution functions. The measurements are consistent with the standard model expectations.