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Heegard and Berger introduced the model of lossy source coding in which side information is available at many decoders. For this model, their showed an upper bound of the rate-distortion function in the case where the source is stationary memoryless. In this paper, we extend their model to the case where the source may be nonstationary and/or nonergodic, and clarify the rate-distortion function for this model. This result is based on the information-spectrum method introduced by Han and Verdú. We also show some special cases of the rate-distortion function, and a single-letterized upper bound of the rate-distortion function in the case where the source is stationary memoryless.