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Oxygen K-edge absorption spectra of carefully characterized La 2− x Sr x CuO 4+ δ samples were measured using a bulk-sensitive fluoresence-yield-detection method. They reveal two distinct pre-edge peaks which evolve systematically as a function of Sr concentration. The measured spectra are quantitatively described by calculations based on the Hubbard model, including local Coulomb interactions and core-hole excitonic correlations. The absorption data are consistent with a description of electronic states based on a doped charge-transfer insulator.