A Local Ratio Theorem
Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 545-552
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Let Tt, t > 0, be a strongly continuous semigroup of positive linear contractions on the L 1-space of a σ-finite measure space . We denote the integral ∫0 t T s ƒ ds, ƒ ∈ L 1, by S 0t ƒ, which is denned as the limit of Riemann sums, in the norm topology of L 1. It is easy to see that, given ƒ ∈ L 1 +, there exists a function F on the product space X× (0, ∞), measurable with respect to the usual product σ-field, such that for every t ≧ 0, ∫0tF(·, s) ds gives a representation of S 0t ƒ. We write S 0t ƒ(x) for ∫0t F(x, S) ds, with a fixed choice of F.
Akcoglu, M. A.; Chacon, R. V. A Local Ratio Theorem. Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 545-552. doi: 10.4153/CJM-1970-062-2
@article{10_4153_CJM_1970_062_2,
author = {Akcoglu, M. A. and Chacon, R. V.},
title = {A {Local} {Ratio} {Theorem}},
journal = {Canadian journal of mathematics},
pages = {545--552},
year = {1970},
volume = {22},
number = {3},
doi = {10.4153/CJM-1970-062-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-062-2/}
}
[1] 1. Akcoglu, M. A., An ergodic lemma, Proc. Amer. Math. Soc. 16 (1965), 388–392. Google Scholar
[2] 2. Chacon, R. V. and Ornstein, D. S., A general ergodic theorem, Illinois J. Math. 4 (I960), 153–160. Google Scholar
[3] 3. Krengel, U., A local ergodic theorem, Invent. Math. 6 (1969), 329–333. Google Scholar
[4] 4. Ornstein, D. S., A ratio martingale theorem and another general ergodic theorem (to appear). Google Scholar
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