Geodesic
An ergodic theorem for additive functionals
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 3, pp. 625-628 
Yu. V. Direev. An ergodic theorem for additive functionals. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 3, pp. 625-628. http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a19/
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     author = {Yu. V. Direev},
     title = {An ergodic theorem for additive functionals},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a19/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a class of Markov processes M. Fukushima ([1]) and M. G. Sur ([2] and [3]) have proposed the description of the exceptional set in Chacon–Ornstein's theorem. In the paper a generalisation of these results for the case of additive functionals of Markov processes are given.