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The ergodic theory of positive operators on continuous functions. (English) Zbl 0258.47010


MSC:

47A35 Ergodic theory of linear operators
28D05 Measure-preserving transformations
60F15 Strong limit theorems
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References:

[1] Dunford N. , and Schwartz , J.T. , Linear operators Parte I . Interscience Ptiblisbers , New York , 1958 . Zbl 0084.10402 · Zbl 0084.10402
[2] Yosida K. , and Hewitt , E. , Finitely additive rzeasures , Trans. Amer. Math. Soc. 72 , 46 - 66 ( 1952 ). MR 45194 | Zbl 0046.05401 · Zbl 0046.05401 · doi:10.2307/1990654
[3] Neveu , J. , Mathematical foundations of the calculus of piobability , Holden-Day , San Francisco . Zbl 0137.11301 · Zbl 0137.11301
[4] Foguel , S.R. , Ergodic decorrzposition of a topologioal space , Israel J. of Math. vol. 7 ( 1969 ) 164 - 167 . MR 249570 | Zbl 0179.08302 · Zbl 0179.08302 · doi:10.1007/BF02771663
[5] Horowitz S. , Markov processes on a locally compact 8pac6 , to be published. · Zbl 0216.47102
[6] Lin , M. , Conservative Markov processes on a topological space . Israel J. of Math. MR 265559 | Zbl 0219.60005 · Zbl 0219.60005 · doi:10.1007/BF02771312
[7] Meyer , P.A. , Theoi-io ergodiquo et potentiels , Annales de l’istitute Fourier ( Grenoble ) Vol. 15 , 1 , 89 - 96 ( 1965 ). Numdam | MR 200413
[8] Chung , K.L. , The general theory of Markov processes aocording to Doeblin , Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete , Band 2 ( 1963-68 ), pp. 230 - 254 . MR 166835 | Zbl 0119.34604 · Zbl 0119.34604 · doi:10.1007/BF00533381
[9] Foguel , S.R. , Ergodic decompositdon of a topological space , Israel J. of Nath. Zbl 0179.08302 · Zbl 0179.08302 · doi:10.1007/BF02771663
[10] Horowitz , S. , Markov processes on a locally compact space , Israel J. of Math , 7 ( 1969 ), 311 - 324 . MR 264759 | Zbl 0216.47102 · Zbl 0216.47102 · doi:10.1007/BF02788864
[11] Kelley , J.L. , General topology , D. Van Nostrand Co. , New York , 1955 . MR 70144 | Zbl 0066.16604 · Zbl 0066.16604
[12] Lin , M. , Conservative Markov processes on a topological space , Israel J. of Math. 8 ( 1970 ), 165 - 186 . MR 265559 | Zbl 0219.60005 · Zbl 0219.60005 · doi:10.1007/BF02771312
[13] Ffogufl , S.R. , Existence of invariant measures for Markov prooesses , Proe. Amer. Math. Soc. 13 , 833 - 838 ( 1962 ). MR 145590 | Zbl 0126.33901 · Zbl 0126.33901 · doi:10.2307/2034070
[14] Foguel , S.R. , Existenoe of invariant measures for Markov processes II . Proc. Amer. Math. Soc. 17 , 387 - 389 ( 1966 ). MR 193673 | Zbl 0168.16405 · Zbl 0168.16405 · doi:10.2307/2035173
[15] Foguel , S.R. , Positive operators on C (X) , to appear in the Proc. Amer. Math. Soc. [4] Lin , M. , Conservative Markov processes on a topological space , hrael J. of Math. MR 243570 · Zbl 0179.23604
[16] Halmos , P.R. , Measure theorem , Van Nostrand , 1950 . MR 33869 | Zbl 0040.16802 · Zbl 0040.16802
[17] Lin M. , Conservatiroa Markov processes on a topological space , Israel. J. of Math. 8 ( 1970 ), 165 - 186 . MR 265559 | Zbl 0219.60005 · Zbl 0219.60005 · doi:10.1007/BF02771312
[18] Foguel , S.R. , Ratio limit theorems for Markov processes , Israel J. of Math. , vol. 7 , ( 1969 ). MR 260017 | Zbl 0235.60069 · Zbl 0235.60069 · doi:10.1007/BF02788871
[19] Kingman , J.F.C. and Orey , S. , Ratio limit theorems for Markov chains , Proc. Amer. Math. Soc. 15 , 907 - 910 ( 1964 ). MR 173290 | Zbl 0131.16701 · Zbl 0131.16701 · doi:10.2307/2034907
[20] Lin , M. , Invariant measures and ratio limit theorems for Mat-kovproce88e8 , to be published.
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