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Let be a memoryless correlated source with finite alphabets, and let us imagine that one person, encoder 1, observes only and another person, encoder 2, observes only . The encoders can produce encoding functions and respectively, which are made available to the decoder. We determine the rate region in case the decoder is interested only in knowing (with small error probability). In Section H of the paper we give a characterization of the capacity region for degraded broadcast channels (DBC's), which was conjectured by Bergmans  and is somewhat sharper than the one obtained by Gallager .