Ergodic theorems and weak mixing for Markov processes

Ryotaro SATO

doi:10.2969/jmsj/02520257

Ryotaro SATO

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1973 Volume 25 Issue 2 Pages 257-264

DOI https://doi.org/10.2969/jmsj/02520257

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Published: 1973 Received: February 09, 1972 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. R. Blum, A note on mixing transformations, Israel J. Math., 9 (1971), 464-465.
2) A. Brunel and M. Keane, Ergodic theorems for operator sequences, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 12 (1969), 231-240.
3) J. W. England and N. F. G. Martin, On weak mixing metric automorphisms, Bull. Amer. Math. Soc., 74 (1968), 505-507.
4) S. R. Foguel, The ergodic theory of Markov processes, Van Nostrand, New York, 1969.
5) D. L. Hanson and G. Pledger, On the mean ergodic theorem for weighted averages, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 13 (1969), 141-149.
6) U. Krengel and L. Sucheston, On mixing in infinite measure spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 13 (1969), 150-164.
7) M. Lin, Mixing for Markov operators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 19 (1971), 231-242.
8) R. Sato, On the individual ergodic theorem for subsequences, Studia Math., (to appear).
9) R. Sato, On a decomposition of transformations in infinite measure spaces, Pacific J. Math., (to appear).
10) R. Sato, Abel-ergodic theorems for subsequences, Pacific J. Math., (to appear).
11) K. Yosida, Functional analysis, Springer, Berlin-Göttingen-Heidelberg, 1965.

Right : [1] J. R. Blum, A note on mixing transformations, Israel J. Math., 9 (1971), 464-465.
[2] A. Brunel and M. Keane, Ergodic theorems for operator sequences, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 12 (1969), 231-240.
[3] J. W. England and N. F. G. Martin, On weak mixing metric automorphisms, Bull. Amer. Math. Soc., 74 (1968), 505-507.
[4] S. R. Foguel, The ergodic theory of Markov processes, Van Nostrand, New York, 1969.
[5] D. L. Hanson and G. Pledger, On the mean ergodic theorem for weighted averages, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 13 (1969), 141-149.
[6] U. Krengel and L. Sucheston, On mixing in infinite measure spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 13 (1969), 150-164.
[7] M. Lin, Mixing for Markov operators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 19 (1971), 231-242.
[8] R. Sato, On the individual ergodic theorem for subsequences, Studia Math., (to appear).
[9] R. Sato, On a decomposition of transformations in infinite measure spaces, Pacific J. Math., (to appear).
[10] R. Sato, Abel-ergodic theorems for subsequences, Pacific J. Math., (to appear).
[11] K. Yosida, Functional analysis, Springer, Berlin-Göttingen-Heidelberg, 1965.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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