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Borel automorphisms
with no finite invariant measure

Authors: S. Eigen, A. Hajian and B. Weiss
Journal: Proc. Amer. Math. Soc. 126 (1998), 3619-3623
MSC (1991): Primary 28D99
MathSciNet review: 1458869
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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 [Enhancements On Off] (What's this?)

  • 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

A. Hajian

B. Weiss
Affiliation: Department of Mathematics, The Hebrew University of Jerusalem, Institute of Mathematics, Givat Ram 91904 Jerusalem, Israel

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
Article copyright: © Copyright 1998 American Mathematical Society

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