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Ergodic sets
Author:
John C. Oxtoby
Journal:
Bull. Amer. Math. Soc. 58 (1952), 116-136
MathSciNet review:
0047262
Full-text PDF
References |
Additional Information
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C. Oxtoby and S.
M. Ulam, On the existence of a measure invariant under a
transformation, Ann. of Math. (2) 40 (1939),
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space, Math. Japonicae 1 (1948), 99–103. MR 0030717
(11,41b)
- 1.
- W. Ambrose and S. Kakutani, Structure and continuity of measurable flows, Duke Math. J. vol. 9 (1942) pp. 25-42. MR 5800
- 2.
- W. Ambrose, P. R. Halmos, and S. Kakutani, The decomposition of measures II, Duke Math. J. vol. 9 (1942) pp. 43-47. MR 5801
- 3.
- J. Dieudonné, Sur le théorème de Lebesgue-Nikodým (III), Annales de l'Université de Grenoble vol. 23 (1948) pp. 25-53. MR 28924
- 4.
- S. Fomin, Finite invariant measures in the flows, Rec. Math. (Mat. Sbornik) N.S. vol. 12 (1943) pp. 99-108. MR 9097
- 5.
- S. Fomin, On measures invariant under certain groups of transformations, Iz-vestiya Akad. Nauk SSSR, Ser. Mat. vol. 14 (1950) pp. 261-274. MR 35925
- 6.
- S. Fomin, On dynamical systems with pure point spectrum, Doklady Akad. Nauk SSSR. vol. 77 (1951) pp. 29-32. MR 43397
- 7.
- M. Garcia and G. A. Hedlund, The structure of minimal sets, Bull. Amer. Math. Soc. vol. 54 (1948) pp. 954-964. MR 26764
- 8.
- W. H. Gottschalk, Almost periodic points with respect to transformation semigroups, Ann. of Math. vol. 47 (1946) pp. 762-766. MR 17475
- 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. MR 4718
- 11.
- P. R. Halmos, On a theorem of Dieudonné, Proc. Nat. Acad. Sci. U.S.A. vol. 35 (1949) pp. 38-42. MR 27832
- 12.
- P. R. Halmos, Measure theory, New York, 1950. MR 33869
- 13.
- P. R. Halmos and J. von Neumann, Operator methods in classical mechanics, II, Ann. of Math. vol. 43 (1942) pp. 332-350. MR 6617
- 14.
- P. Hartman and A. Wintner, Asymptotic distributions and the ergodic theorem, Amer. J. Math. vol. 61 (1939) pp. 977-984. MR 353
- 15.
- G. A. Hedlund, Sturmian minimal sets, Amer. J. Math. vol. 66 (1944) pp. 605-620. MR 10792
- 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. MR 1503326
- 17.
- C. Kuratowski, Topologie I, 2d ed., Warszawa-Wroclaw, 1948. MR 28007
- 18.
- D. Maharam, Decompositions of measure algebras and spaces, Trans. Amer. Math. Soc. vol. 69 (1950) pp. 142-160. MR 36817
- 19.
- M. Morse, Recurrent geodesics on a surface of negative curvature, Trans. Amer. Math. Soc. vol. 22 (1921) pp. 84-100. MR 1501161
- 20.
- M. Morse and G. A. Hedlund, Symbolic dynamics, Amer. J. Math. vol. 60 (1938) pp. 815-866. MR 1507944
- 21.
- M. Morse and G. A. Hedlund, Symbolic dynamics II. Sturmian trajectories, Amer. J. Math. vol. 62 (1940) pp. 1-42. MR 745
- 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. MR 9788
- 23.
- V. V. Nemyckiĭ and V. V. Stepanov, Qualitative theory of differential equations, 2d ed., Moscow, 1949.
- 24.
- J. von Neumann, Zur Operatorenmethode in der klassischen Mechanik, Ann. of Math. vol. 33 (1932) pp. 587-642. MR 1503078
- 25.
- O. M. Nikodým, Tribus de Boole et fonctions mesurables, C. R. Acad. Sci. Paris vol. 228 (1949) pp. 150-151. MR 27834
- 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. MR 97
- 27.
- H. E. Robbins, On a class of recurrent sequences, Bull. Amer. Math. Soc. vol. 43 (1937) pp. 413-417.
- 28.
- S. Saks, Integration in abstract metric spaces, Duke Math. J. vol. 4 (1938) pp. 408-411. MR 1546062
- 29.
- K. Yosida, Simple Markoff process with a locally compact phase space, Mathematica Japonicae vol. 1 (1948) pp. 99-103. MR 30717
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1952-09580-X
PII:
S 0002-9904(1952)09580-X
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