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Borel automorphisms with no finite invariant measure
Author(s):
S.
Eigen;
A.
Hajian;
B.
Weiss
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3619-3623.
MSC (1991):
Primary 28D99
MathSciNet review:
1458869
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Abstract:
An uncountable family of non-isomorphic Borel automorphisms which do not preserve any finite measure is presented.
References:
- 1.
- S. Eigen, A. Hajian and Y. Ito, Ergodic measure preserving transformations of finite type, Tokyo J. of Math 110, (1988) 459-470. MR 90b:28017
- 2.
- S. Eigen, A. Hajian and S. Kakutani, Complementing sets of integers - a result from ergodic theory. Japanese J. Math. 18, No. 1, (1992) 205-211. MR 93g:11087
- 3.
- S. Eigen, A. Hajian and M.G. Nadkarni, Weakly wandering sets and compressibility in descriptive setting, Proc. Indian Acad. Sci. 103, (1993) 321-327. MR 95g:28028
- 4.
- A. Hajian and S. Kakutani, Weakly wandering sets and invariant measures, Trans. Amer. Math. Soc. 110 (1964) 136-151. MR 27:4904
- 5.
- M.G. Nadkarni, Descriptive ergodic theory, in Contemporary Mathematics 94, American Math. Society, (1989) 191-206. MR 90h:28021
- 6.
- B. Weiss, Measurable dynamics in Contemporary Mathematics Volume 26, American Math. Society, (1984) 395-421. MR 85j:28027
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Additional Information:
S.
Eigen
Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email:
eigen@neu.edu
A.
Hajian
Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email:
hajian@neu.edu
B.
Weiss
Affiliation:
Department of Mathematics, The Hebrew University of Jerusalem, Institute of Mathematics, Givat Ram 91904 Jerusalem, Israel
Email:
weiss@math.huji.ac.il
DOI:
10.1090/S0002-9939-98-04489-X
PII:
S 0002-9939(98)04489-X
Keywords:
Borel automorphisms,
ergodic theory
Received by editor(s):
January 15, 1997
Received by editor(s) in revised form:
April 23, 1997
Communicated by:
Mary Rees
Copyright of article:
Copyright
1998,
American Mathematical Society
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