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A general local ergodic theorem. (English) Zbl 0254.47013


MSC:

47A35 Ergodic theory of linear operators
28D05 Measure-preserving transformations
47D03 Groups and semigroups of linear operators
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References:

[1] M. A. Akcoglu and R. V. Chacon: A local ratio theorem. Canad. J. Math., 22, 545-552 (1970). · Zbl 0201.06603
[2] R. Chacon and D. Ornstein: A general ergodic theorem. 111. J. Math., 4, 153-160 (1960). · Zbl 0134.12102
[3] N. Dunford and J. T. Schwartz: Linear Operators. I. Interscience (1958). · Zbl 0084.10402
[4] H. Fong and L. Sucheston: On the ratio ergodic theorem for semi-groups. Pacific J. Math., 39, 659-667 (1971). · Zbl 0228.28012
[5] U. Krengel: A local ergodic theorem. Inventiones Math., 6, 329-333 (1969). · Zbl 0165.37402
[6] D. Ornstein: The sum of iterates of a positive operator. Advances in Probability and Related Topics (Edited by P. Ney), 2, 87-115 (1970). · Zbl 0321.28013
[7] T. R. Terrell: Local ergodic theorem for ^-parameter semi-groups of operators. Lecture Notes in Math., No. 160, 262-278 (1970). Springer-Verlag. · Zbl 0204.45406
[8] S. Tsurumi: Ergodic theorems (in Japanese). Sugaku, 13, 80-88 (1961/ 62). · Zbl 0126.08201
[9] K. Yosida: Functional Analysis. Springer-Verlag (1965). · Zbl 0126.11504
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