A Multiple Sequence Ergodic Theorem
1983 ◽
Vol 26
(4)
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pp. 493-497
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Keyword(s):
AbstractLet be a σ-finite measure space, {T1, …, Tk} a set of linear operators of , some p, 1≤p≤∞.Ifexists 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}.
Keyword(s):
1980 ◽
Vol 23
(1)
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pp. 115-116
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Keyword(s):
1981 ◽
Vol 24
(2)
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pp. 199-203
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Keyword(s):
1976 ◽
Vol 28
(5)
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pp. 1073-1075
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Keyword(s):
1979 ◽
Vol 31
(2)
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pp. 441-447
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Keyword(s):
1977 ◽
Vol 24
(2)
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pp. 129-138
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1985 ◽
Vol 8
(3)
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pp. 433-439
1965 ◽
Vol 61
(2)
◽
pp. 497-498
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