Geodesic
An ergodic theorem for Markov processes.~I
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 410-416

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For a class of Markov processes, M. Fukushima [3] proposed a description of the exceptional set in Chacon–Ornstein's theorem. In the paper, a generalization of this result is given. 
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     author = {M. G. \v{S}ur},
     title = {An ergodic theorem for {Markov} {processes.~I}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a19/}
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M. G. Šur. An ergodic theorem for Markov processes.~I. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 410-416. http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a19/