Geodesic
The Individual Ergodic Theorem for Contractions with Fixed Points
Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 115-116

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Let (X, I, μ) be a σ-finite measure space and let T take L p to L p, p fixed, 1<p<∞,‖t‖p≤1. We shall say that the individual ergodic theorem holds for T if for any uniform sequence K1, k2,... (for the definition, see [2]) and for any f∊LP(X), the limit exists and is finite almost everywhere. 
Olsen, James H. The Individual Ergodic Theorem for Contractions with Fixed Points. Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 115-116. doi: 10.4153/CMB-1980-017-3
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     author = {Olsen, James H.},
     title = {The {Individual} {Ergodic} {Theorem} for {Contractions} with {Fixed} {Points}},
     journal = {Canadian mathematical bulletin},
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     year = {1980},
     volume = {23},
     number = {1},
     doi = {10.4153/CMB-1980-017-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-017-3/}
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