Geodesic
A Dominated Ergodic Theorem for Contractions with Fixed Points
Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 89-91

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Let be a finite measure space, and let T be a contraction in real Lp (X). (i.e. T is linear and ||T||≤1). It is said that the Dominated Ergodic Theorem holds for T, if there exists a constant cp such that, if M(T)f(x) = supn 1/n then ||M(T)f||p ≤ cp ||f||p for every f in Lp . 
Torre, A. De La. A Dominated Ergodic Theorem for Contractions with Fixed Points. Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 89-91. doi: 10.4153/CMB-1977-014-5
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     author = {Torre, A. De La},
     title = {A {Dominated} {Ergodic} {Theorem} for {Contractions} with {Fixed} {Points}},
     journal = {Canadian mathematical bulletin},
     pages = {89--91},
     year = {1977},
     volume = {20},
     number = {1},
     doi = {10.4153/CMB-1977-014-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-014-5/}
}
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