Akcoglu's Ergodic Theorem for Uniform Sequences
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Let (X, F,) be a sigma-finite measure space. In what follows we assume p fixed, 1 < p < ∞ . Let T be a contraction of Lp(X, F, μ) (‖T‖,p ≦ 1). If ƒ ≧ 0 implies Tƒ ≧ 0 we will say that T is positive. In this paper we prove that if is a uniform sequence (see Section 2 for definition) and T is a positive contraction of Lp, thenexists and is finite almost everywhere for every ƒ ∊ Lp(X, F, μ).
1980 ◽
Vol 23
(1)
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pp. 115-116
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1981 ◽
Vol 24
(2)
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pp. 199-203
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1976 ◽
Vol 28
(5)
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pp. 1073-1075
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1983 ◽
Vol 26
(4)
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pp. 493-497
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1974 ◽
Vol 26
(5)
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pp. 1206-1216
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1979 ◽
Vol 31
(2)
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pp. 441-447
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1977 ◽
Vol 24
(2)
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pp. 129-138
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1975 ◽
Vol 27
(5)
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pp. 1075-1082
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