Ergodic sets
John C. Oxtoby
Source: Bull. Amer. Math. Soc. Volume 58, Number 2
(1952), 116-136.
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Permanent link to this document: http://projecteuclid.org/euclid.bams/1183516689
Mathematical Reviews number (MathSciNet): MR0047262
Zentralblatt MATH identifier: 0046.11504
References
1. W. Ambrose and S. Kakutani, Structure and continuity of measurable flows, Duke Math. J. vol. 9 (1942) pp. 25-42.
Zentralblatt MATH: 0063.00065
Mathematical Reviews (MathSciNet): MR5800
Digital Object Identifier: doi:10.1215/S0012-7094-42-00904-9
Project Euclid: euclid.dmj/1077493068
2. W. Ambrose, P. R. Halmos, and S. Kakutani, The decomposition of measures II, Duke Math. J. vol. 9 (1942) pp. 43-47.
Zentralblatt MATH: 0063.00066
Mathematical Reviews (MathSciNet): MR5801
Digital Object Identifier: doi:10.1215/S0012-7094-42-00905-0
Project Euclid: euclid.dmj/1077493069
3. J. Dieudonné, Sur le théorème de Lebesgue-Nikodým (III), Annales de l'Université de Grenoble vol. 23 (1948) pp. 25-53.
Zentralblatt MATH: 0030.16002
Mathematical Reviews (MathSciNet): MR28924
4. S. Fomin, Finite invariant measures in the flows, Rec. Math. (Mat. Sbornik) N.S. vol. 12 (1943) pp. 99-108.
Zentralblatt MATH: 0063.01405
Mathematical Reviews (MathSciNet): MR9097
5. S. Fomin, On measures invariant under certain groups of transformations, Iz-vestiya Akad. Nauk SSSR, Ser. Mat. vol. 14 (1950) pp. 261-274.
Zentralblatt MATH: 0037.07501
Mathematical Reviews (MathSciNet): MR35925
6. S. Fomin, On dynamical systems with pure point spectrum, Doklady Akad. Nauk SSSR. vol. 77 (1951) pp. 29-32.
Zentralblatt MATH: 0045.38803
Mathematical Reviews (MathSciNet): MR43397
7. M. Garcia and G. A. Hedlund, The structure of minimal sets, Bull. Amer. Math. Soc. vol. 54 (1948) pp. 954-964.
Zentralblatt MATH: 0032.36002
Mathematical Reviews (MathSciNet): MR26764
Digital Object Identifier: doi:10.1090/S0002-9904-1948-09113-3
Project Euclid: euclid.bams/1183512387
8. W. H. Gottschalk, Almost periodic points with respect to transformation semigroups, Ann. of Math. vol. 47 (1946) pp. 762-766.
Zentralblatt MATH: 0063.01713
Mathematical Reviews (MathSciNet): MR17475
Digital Object Identifier: doi:10.2307/1969233
9. H. Hahn, Theorie der reellen Funktionen, I, Berlin, 1921.
10. P. R. Halmos, The decomposition of measures, Duke Math. J. vol. 8 (1941) pp. 386-392.
Mathematical Reviews (MathSciNet): MR4718
Digital Object Identifier: doi:10.1215/S0012-7094-41-00830-X
Project Euclid: euclid.dmj/1077492653
11. P. R. Halmos, On a theorem of Dieudonné, Proc. Nat. Acad. Sci. U.S.A. vol. 35 (1949) pp. 38-42.
Zentralblatt MATH: 0031.40701
Mathematical Reviews (MathSciNet): MR27832
Digital Object Identifier: doi:10.1073/pnas.35.1.38
12. P. R. Halmos, Measure theory, New York, 1950.
Zentralblatt MATH: 0040.16802
Mathematical Reviews (MathSciNet): MR33869
13. P. R. Halmos and J. von Neumann, Operator methods in classical mechanics, II, Ann. of Math. vol. 43 (1942) pp. 332-350.
Zentralblatt MATH: 0063.01888
Mathematical Reviews (MathSciNet): MR6617
Digital Object Identifier: doi:10.2307/1968872
14. P. Hartman and A. Wintner, Asymptotic distributions and the ergodic theorem, Amer. J. Math. vol. 61 (1939) pp. 977-984.
Mathematical Reviews (MathSciNet): MR353
Digital Object Identifier: doi:10.2307/2371642
15. G. A. Hedlund, Sturmian minimal sets, Amer. J. Math. vol. 66 (1944) pp. 605-620.
Zentralblatt MATH: 0063.01982
Mathematical Reviews (MathSciNet): MR10792
Digital Object Identifier: doi:10.2307/2371769
16. N. Kryloff and N. Bogoliouboff, La théorie générale de la mesure dans son application à l'étude des systèmes dynamiques de la mécanique non linéaire, Ann. of Math. vol. 38 (1937) pp. 65-113.
Mathematical Reviews (MathSciNet): MR1503326
Digital Object Identifier: doi:10.2307/1968511
17. C. Kuratowski, Topologie I, 2d ed., Warszawa-Wroclaw, 1948.
Zentralblatt MATH: 0078.14603
Mathematical Reviews (MathSciNet): MR28007
18. D. Maharam, Decompositions of measure algebras and spaces, Trans. Amer. Math. Soc. vol. 69 (1950) pp. 142-160.
Zentralblatt MATH: 0041.18002
Mathematical Reviews (MathSciNet): MR36817
19. M. Morse, Recurrent geodesics on a surface of negative curvature, Trans. Amer. Math. Soc. vol. 22 (1921) pp. 84-100.
Mathematical Reviews (MathSciNet): MR1501161
Digital Object Identifier: doi:10.1090/S0002-9947-1921-1501161-8
20. M. Morse and G. A. Hedlund, Symbolic dynamics, Amer. J. Math. vol. 60 (1938) pp. 815-866.
Mathematical Reviews (MathSciNet): MR1507944
Digital Object Identifier: doi:10.2307/2371264
21. M. Morse and G. A. Hedlund, Symbolic dynamics II. Sturmian trajectories, Amer. J. Math. vol. 62 (1940) pp. 1-42.
Mathematical Reviews (MathSciNet): MR745
Digital Object Identifier: doi:10.2307/2371431
22. M. Morse and G. A. Hedlund, Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J. vol. 11 (1944) pp. 1-7.
Zentralblatt MATH: 0063.04115
Mathematical Reviews (MathSciNet): MR9788
Digital Object Identifier: doi:10.1215/S0012-7094-44-01101-4
Project Euclid: euclid.dmj/1077472364
23. V. V. Nemyckiĭ and V. V. Stepanov, Qualitative theory of differential equations, 2d ed., Moscow, 1949.
Zentralblatt MATH: 0089.29502
24. J. von Neumann, Zur Operatorenmethode in der klassischen Mechanik, Ann. of Math. vol. 33 (1932) pp. 587-642.
Zentralblatt MATH: 0005.12203
Mathematical Reviews (MathSciNet): MR1503078
Digital Object Identifier: doi:10.2307/1968537
25. O. M. Nikodým, Tribus de Boole et fonctions mesurables, C. R. Acad. Sci. Paris vol. 228 (1949) pp. 150-151.
Zentralblatt MATH: 0041.18001
Mathematical Reviews (MathSciNet): MR27834
26. J. C. Oxtoby and S. M. Ulam, On the existence of a measure invariant under a transformation, Ann. of Math. vol. 40 (1939) pp. 560-566.
Zentralblatt MATH: 0021.41202
Mathematical Reviews (MathSciNet): MR97
Digital Object Identifier: doi:10.2307/1968940
27. H. E. Robbins, On a class of recurrent sequences, Bull. Amer. Math. Soc. vol. 43 (1937) pp. 413-417.
Mathematical Reviews (MathSciNet): MR1563552
Digital Object Identifier: doi:10.1090/S0002-9904-1937-06568-2
Project Euclid: euclid.bams/1183499841
28. S. Saks, Integration in abstract metric spaces, Duke Math. J. vol. 4 (1938) pp. 408-411.
Zentralblatt MATH: 0019.17004
Mathematical Reviews (MathSciNet): MR1546062
Digital Object Identifier: doi:10.1215/S0012-7094-38-00433-8
Project Euclid: euclid.dmj/1077490647
29. K. Yosida, Simple Markoff process with a locally compact phase space, Mathematica Japonicae vol. 1 (1948) pp. 99-103.
Zentralblatt MATH: 0041.25105
Mathematical Reviews (MathSciNet): MR30717
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