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We present a measurement of the tt¯ production cross section σtt¯ in pp¯ collisions at s=1.96 TeV using 5.4 fb−1 of integrated luminosity collected with the D0 detector. We consider final states with at least two jets and two leptons (ee, eμ, μμ), and events with one jet for the eμ final state as well. The measured cross section is σtt¯=7.36−0.79+0.90(stat+syst) pb. This result combined with the cross section measurement in the lepton+jets final state yields σtt¯=7.56−0.56+0.63(stat+syst) pb, which agrees with the standard model expectation. The relative precision of 8% of this measurement is comparable to the precision of the latest theoretical calculations.