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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Akcoglu, M. A., A Pointwise Ergodic Theorem in L-Spaces, Can. J. Math. 27 (1975), 1075-1082. Google Scholar

[2] 2. Brunei, A. and Keane, M., Ergodic Theorems for Operator Sequences, Z. Wahrscheinlichkeitstheorie Veru. Geb. 12 (1969), pp. 231-240. Google Scholar

[3] 3. De La Torre, A., A dominated Ergodic Theorem for Contractions with Fixed Points, Canad. Math. Bull., 20 (1977), 89-91. Google Scholar

[4] 4. Sato, R., On the Individual Ergodic Theorem for Subsequences, Studia Mathematica, T. 45 (1973), 31-35. Google Scholar

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