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If is a sequence of independent identically distributed discrete random pairs with , Slepian and Wolf have shown that the process and the process can be separately described to a common receiver at rates and hits per symbol if . A simpler proof of this result will be given. As a consequence it is established that the Slepian-Wolf theorem is true without change for arbitrary ergodic processes and countably infinite alphabets. The extension to an arbitrary number of processes is immediate.