Published: 1977 Received: February 18, 1974Available on J-STAGE: October 20, 2006Accepted: -
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Date of correction: October 20, 2006Reason for correction: -Correction: CITATIONDetails: Wrong : 1) M.A. Akcoglu and J. Cunsolo, An ergodic theorem for semigroups, Proc. Amer. Math. Soc., 24 (1970), 161-170. 2) K.N. Berk, Ergodic theory with recurrent weights, Ann. of Math. Statist., 39 (1968), 1107-1114. 3) R.V. Chacon and D.S. Ornstein, A general ergodic theorem, Illinois J. Math., 4 (1960), 153-160. 4) Y. Derriennic and M. Lin, On invariant measures and ergodic theorems for positive operators, J. Functional Analysis, 13 (1973), 252-267. 5) N. Dunford and J. T. Schwartz, Convergence almost everywhere of operator averages, J. Rational Mech. Anal., 5 (1956), 129-178. 6) N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience Publishers, New York, 1958. 7) H. Fong and L. Sucheston, On the ratio ergodic theorem for semi-groups, Pacific J. Math., 39 (1971), 659-667. 8) H. Fong and L. Sucheston, On unaveraged convergence of positive operators in Lebesgue space, Trans. Amer. Math. Soc., 179 (1973), 383-397. 9) S. Hasegawa and R. Sato, A general ratio ergodic theorem for semigroups, Pacific J. Math., 62 (1976), 435-437. 10) G. Helmberg, On the converse of Hopf's ergodic theorem, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 21 (1972), 77-80. 11) Y. Kubokawa, Ergodic theorems for contraction semi-groups, J. Math. Soc. Japan, 27 (1975), 184-193. 12) M. Lin, Semi-groups of Markov operators, Boll. Un. Mat. Ital., (4) 6 (1972), 20-44. 13) R. Sato, On the individual ergodic theorem for positive operators, Proc. Amer. Math. Soc., 36 (1972), 456-458. 14) R. Sato, Ergodic properties of bounded L1-operators, Proc. Amer. Math. Soc., 39 (1973), 540-546. 15) R. Sato, Invariant measures for semigroups, Studia Math., 53 (1975), 129-134. 16) R. Sato, A mean ergodic theorem, Amer. Math. Monthly, 82 (1975), 487-488. 17) S. Tsurumi, An ergodic theorem for a semigroup of linear contractions, Proc. Japan Acad., 49 (1973), 306-309. 18) K. Yosida, Functional analysis, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965. 19) K. Yosida and S. Kakutani, Operator-theoretical treatment of Markoff's process and mean ergodic theorem, Ann. of Math., (2) 42 (1941), 188-228.
Right : [1] M. A. Akcoglu and J. Cunsolo, An ergodic theorem for semigroups, Proc. Amer. Math. Soc., 24 (1970), 161-170. [2] K. N. Berk, Ergodic theory with recurrent weights, Ann. of Math. Statist., 39 (1968), 1107-1114. [3] R. V. Chacon and D. S. Ornstein, A general ergodic theorem, Illinois J. Math., 4 (1960), 153-160. [4] Y. Derriennic and M. Lin, On invariant measures and ergodic theorems for positive operators, J. Functional Analysis, 13 (1973), 252-267. [5] N. Dunford and J. T. Schwartz, Convergence almost everywhere of operator averages, J. Rational Mech. Anal., 5 (1956), 129-178. [6] N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience Publishers, New York, 1958. [7] H. Fong and L. Sucheston, On the ratio ergodic theorem for semi-groups, Pacific J. Math., 39 (1971), 659-667. [8] H. Fong and L. Sucheston, On unaveraged convergence of positive operators in Lebesgue space, Trans. Amer. Math. Soc., 179 (1973), 383-397. [9] S. Hasegawa and R. Sato, A general ratio ergodic theorem for semigroups, Pacific J. Math., 62 (1976), 435-437. [10] G. Helmberg, On the converse of Hopf's ergodic theorem, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 21 (1972), 77-80. [11] Y. Kubokawa, Ergodic theorems for contraction semi-groups, J. Math. Soc. Japan, 27 (1975), 184-193. [12] M. Lin, Semi-groups of Markov operators, Boll. Un. Mat. Ital., (4) 6 (1972), 20-44. [13] R. Sato, On the individual ergodic theorem for positive operators, Proc. Amer. Math. Soc., 36 (1972), 456-458. [14] R. Sato, Ergodic properties of bounded L1-operators, Proc. Amer. Math. Soc., 39 (1973), 540-546. [15] R. Sato, Invariant measures for semigroups, Studia Math., 53 (1975), 129-134. [16] R. Sato, A mean ergodic theorem, Amer. Math. Monthly, 82 (1975), 487-488. [17] S. Tsurumi, An ergodic theorem for a semigroup of linear contractions, Proc. Japan Acad., 49 (1973), 306-309. [18] K. Yosida, Functional analysis, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965. [19] K. Yosida and S. Kakutani, Operator-theoretical treatment of Markoff's process and mean ergodic theorem, Ann. of Math., (2) 42 (1941), 188-228.
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