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We present a method for incorporating the information contained in new datasets into an existing set of parton distribution functions without the need for refitting. The method involves reweighting the ensemble of parton densities through the computation of the chi-square to the new dataset. We explain how reweighting may be used to assess the impact of any new data or pseudodata on parton densities and thus on their predictions. We show that the method works by considering the addition of inclusive jet data to a DIS+DY fit, and comparing to the refitted distribution. We then use reweighting to determine the impact of recent high statistics lepton asymmetry data from the D0 experiment on the NNPDF2.0 parton set. We find that the D0 inclusive muon and electron data are perfectly compatible with the rest of the data included in the NNPDF2.0 analysis and impose additional constraints on the large-x d/u ratio. The more exclusive D0 electron datasets are however inconsistent both with the other datasets and among themselves, suggesting that here the experimental uncertainties have been underestimated.