Geodesic
Skew products and ergodic theorems for group actions
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 13-28 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain new ergodic theorems for an action of the free semi-group on a probability space by measure-preserving maps. Our method consists in associating with the original semi-group action a skew product over the shift on the space of infinite one-sided sequences of generators of the semi-group, and then integrating Birkhoff–Khinchin ergodic theorems along the base of the skew product. 
@article{ZNSL_2000_266_a2,
     author = {A. I. Bufetov},
     title = {Skew products and ergodic theorems for group actions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {13--28},
     year = {2000},
     volume = {266},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a2/}
}
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A. I. Bufetov. Skew products and ergodic theorems for group actions. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 13-28. http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a2/