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This paper discusses some new results related to ergodic and limit theorems and also to the repeated logarithm low for inhomogeneous Markov chains. Theorems are formulated and proved for conditions that were not treated in the literature; some estimates obtained previously by S. N. Bernshtein are employed. Lemma 1 is of greatest importance in the paper.
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T. A. Sarymsakov (1961) studied this question.
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