Abstract
Blackwell and Freedman [2] proved that the exchangeable σ-field ℰ of a homogeneous recurrent Markov chain is atomic. If the chain is finite, the atoms can be found explicitly by means of an algorithm given below. The approach in [2] cannot be extended to a non-homogeneous chain, but a description of ℰ can be obtained in this case by using coupling methods, provided the chain is finite and satisfies certain conditions.
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