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Uniform integrability and the pointwise ergodic theorem
Author:
Yuji Ito
Journal:
Proc. Amer. Math. Soc. 16 (1965), 222-227
MSC:
Primary 28.70
MathSciNet review:
0171895
Full-text PDF Free Access
References |
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Additional Information
- [1]
R.
V. Chacon, A class of linear
transformations, Proc. Amer. Math. Soc. 15 (1964), 560–564.
MR
0165071 (29 #2362), http://dx.doi.org/10.1090/S0002-9939-1964-0165071-7
- [2]
R.
V. Chacon and D.
S. Ornstein, A general ergodic theorem, Illinois J. Math.
4 (1960), 153–160. MR 0110954
(22 #1822)
- [3]
Nelson
Dunford and D.
S. Miller, On the ergodic theorem, Trans. Amer. Math. Soc. 60 (1946), 538–549. MR 0018359
(8,280b), http://dx.doi.org/10.1090/S0002-9947-1946-0018359-8
- [4]
N. Dunford and J. T. Schwartz, Linear operators, Vol. I, Interscience, New York, 1957.
- [5]
Alexandra
Ionescu Tulcea, Un théorème de catégorie dans
la théorie ergodique, C. R. Acad. Sci. Paris
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(27 #4907)
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A.
Ionescu Tulcea, On the category of certain classes of
transformations in ergodic theory, Trans. Amer.
Math. Soc. 114
(1965), 261–279. MR 0179327
(31 #3575), http://dx.doi.org/10.1090/S0002-9947-1965-0179327-0
- [7]
Kôsaku
Yosida and Shizuo
Kakutani, Operator-theoretical treatment of Markoff’s process
and mean ergodic theorem, Ann. of Math. (2) 42
(1941), 188–228. MR 0003512
(2,230e)
- [1]
- R. V. Chacon, A class of linear transformations, Proc. Amer. Math. Soc. 15 (1964), 560-564. MR 0165071 (29:2362)
- [2]
- R. V. Chacon and D. S. Ornstein, A general ergodic theorem, Illinois J. Math. 4 (1960), 153-160. MR 0110954 (22:1822)
- [3]
- N. Dunford and D. S. Miller, On the ergodic theorem, Trans. Amer. Math. Soc. 60 (1946), 538-549. MR 0018359 (8:280b)
- [4]
- N. Dunford and J. T. Schwartz, Linear operators, Vol. I, Interscience, New York, 1957.
- [5]
- A. Ionescu Tulcea, Un théorème de catégorie dans la théorie ergodique, C. R. Acad. Sci. Paris 257 (1963), 18-20. MR 0154964 (27:4907)
- [6]
- -, On the category of certain classes of transformations in ergodic theory, Trans. Amer. Math. Soc. 114 (1965), 261-279. MR 0179327 (31:3575)
- [7]
- 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)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1965-0171895-3
PII:
S 0002-9939(1965)0171895-3
Article copyright:
© Copyright 1965 American Mathematical Society
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