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We present a measurement of e+e− pair production in central PbAu collisions at 158A GeV/c. As reported earlier, a significant excess of the e+e− pair yield over the expectation from hadron decays is observed. The improved mass resolution of the present data set, recorded with the upgraded CERES experiment at the CERN-SPS, allows for a comparison of the data with different theoretical approaches. The data clearly favor a substantial in-medium broadening of the ρ spectral function over a density-dependent shift of the ρ pole mass. The in-medium broadening model implies that baryon induced interactions are the key mechanism to the observed modifications of the ρ meson at SPS energy.