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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

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
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Abstract | References | Similar articles | Additional information

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

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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

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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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