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Transactions of the American Mathematical Society

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Ergodic decompositions induced by certain Markov operators


Author: Benton Jamison
Journal: Trans. Amer. Math. Soc. 117 (1965), 451-468
MSC: Primary 60.60
DOI: https://doi.org/10.1090/S0002-9947-1965-0207041-1
MathSciNet review: 0207041
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  • [1] L. Breiman, The strong law of large numbers for a class of Markov chains, Ann. Math. Statist. 31 (1960), 801-803. MR 0117786 (22:8560)
  • [2] -, On achieving channel capacity in finite memory channels, Illinois J. Math. 4 (1960), 246-252. MR 0118574 (22:9347)
  • [3] W. Doeblin and R. Fortet, Sur les chaînes à liaisons complètes, Bull. Soc. Math. France 65 (1937), 132-148. MR 1505076
  • [4] J. L. Doob, Stochastic processes, Wiley, New York, 1953. MR 0058896 (15:445b)
  • [5] N. Dunford and J. Schwartz, Linear operators, Vol. I, Interscience, New York, 1958.
  • [6] W. Feller, An introduction to probability theory and its applications, 2nd ed., Wiley, New York, 1957. MR 0088081 (19:466a)
  • [7] Harry Furstenberg, Noncommuting random products, Trans. Amer. Math. Soc. 108 (1963), 377-428. MR 0163345 (29:648)
  • [8] -, Strict ergodicity and transformation of the torus, Amer. J. Math. 83 (1961), 573-601. MR 0133429 (24:A3263)
  • [9] C. T. Ionescu Tulcea, On a class of operators occurring in the theory of chains of infinite order, Canad. J. Math. 11 (1959), 112-121. MR 0101569 (21:379)
  • [10] C. T. Ionescu Tulcea and G. Marinescu, Théorie ergodique pour les classes d'opérations non complètement continues, Ann. of Math. (2) 52 (1950), 140-147. MR 0037469 (12:266g)
  • [11] R. Isaac, Markov processes and unique stationary probability measures, Pacific J. Math. 12 (1962), 273-286. MR 0140147 (25:3569)
  • [12] B. Jamison, Asymptotic behavior of iterates of continuous functions under a Markov operator, J. Math. Anal. Appl. 9 (1964), 203-214. MR 0169040 (29:6295)
  • [13] S. Kakutani, Ergodic theory, Proceedings of the International Congress of Mathematicians (Cambridge, Mass., 1950) Vol. 2, pp. 136-139, Amer. Math. Soc., Providence, R. I., 1952. MR 0045947 (13:660f)
  • [14] M. Loève, Probability theory, 2nd ed., Van Nostrand, Princeton, N. J., 1960. MR 0123342 (23:A670)
  • [15] J. Oxtoby, Ergodic sets, Bull. Amer. Math. Soc. 58 (1952), 116-135. MR 0047262 (13:850e)
  • [16] M. Rosenblatt, Equicontinuous Markov operators, Teor. Verojatnost. i Primenen. 9 (1964), 205-222. MR 0171318 (30:1549)
  • [17] K. Yosida, Simple Markov process with a locally compact phase space, Math. Japon. 1 (1948), 99-103. MR 0030717 (11:41b)
  • [18] K. Yosida and S. Kakutani, Operator-theoretical treatment of Markoff's process and mean ergodic theorem, Ann. of Math. (2) 42 (1941), 188-228. MR 0003512 (2:230e)
  • [19] S. P. Lloyd, On certain projections in spaces of continuous functions, Pacific J. Math. 13 (1963), 171-175. MR 0152873 (27:2845)

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DOI: https://doi.org/10.1090/S0002-9947-1965-0207041-1
Article copyright: © Copyright 1965 American Mathematical Society

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