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We present a measurement of the W boson pair-production cross section in pp̅ collisions at a center-of- mass energy of √s = 1.96 TeV. The data, collected with the Run II D0 detector at Fermilab, correspond to an integrated luminosity of 224–252 pb-1 depending on the final state (ℯℯ, ℯμ, or μμ). We observe 25 candidates with a background expectation of 8.1 ± 0.6(stat) ± 0.6(syst) ± 0.5(lum) events. The probability for an upward fluctuation of the background to produce the observed signal is 2.3 x 10-7, equivalent to 5.2 standard deviations. The measurement yields a cross section of 13.8-3.8+4.3 (stat)-0.9+1.2 (syst) ± 0.9(lum) pb, in agreement with predictions from the standard model.