Geodesic
A Multiple Sequence Ergodic Theorem
Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 493-497

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DOI

Let be a σ-finite measure space, {T1, ..., Tk} a set of linear operators of , some p, 1≤p≤∞.If exists a.e. for all f ∊ Lp, we say that the multiple sequence ergodic theorem holds for {T1, ..., Tk}. If f≥0 implies Tf≥0, we say that T is positive. If there exists an operator S such that |Tf(x)|≥S |f|(x) a.e., we say that T is dominated by S. In this paper we prove that if T1, ..., Tk are dominated by positive contractions of , p fixed, 1<p<∞, then the multiple sequence ergodic theorem holds for {T1, ..., Tk}.
DOI : 10.4153/CMB-1983-079-2
Mots-clés : 47A35, 28A65 
Olsen, James H. A Multiple Sequence Ergodic Theorem. Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 493-497. doi: 10.4153/CMB-1983-079-2
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     title = {A {Multiple} {Sequence} {Ergodic} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {493--497},
     year = {1983},
     volume = {26},
     number = {4},
     doi = {10.4153/CMB-1983-079-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-079-2/}
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