Bulletin of the American Mathematical Society

Transformations that do not accept a finite invariant measure

Arshag Hajian and Yuji Ito

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 84, Number 3 (1978), 417-427.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183540624

Mathematical Reviews number (MathSciNet)
MR0466487

Zentralblatt MATH identifier
0398.28019

Subjects
Primary: 28A65 28A70 43A05: Measures on groups and semigroups, etc.

Citation

Hajian, Arshag; Ito, Yuji. Transformations that do not accept a finite invariant measure. Bull. Amer. Math. Soc. 84 (1978), no. 3, 417--427. https://projecteuclid.org/euclid.bams/1183540624


Export citation

References

  • 1. M. H. Ellis and N. A. Friedman, On eventually weakly wandering sequences (to appear).
  • 2. M. H. Ellis and N. A. Friedman, Gap sequences and eventually weakly wandering sequences (to appear).
  • 3. A. Hajian, Strongly recurrent transformations, Pacific J. Math. 14 (1964), 517-523.
  • 4. A. Hajian, On ergodic transformations defined on an infinite measure space, Proc. Amer. Soc 16 (1965), 45-48.
  • 5. A. Hajian and Y. Ito, Iterates of measurable transformations and Markov operators, Trans. Amer. Math. Soc. 17 (1965), 371-386.
  • 6. A. Hajian and Y. Ito, Weakly wandering and related sequences, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 8 (1967), 315-324.
  • 7. A. Hajian, Y. Ito and S. Kakutani, Invariant measures and orbits of dissipative transformations, Advances in Math. 9 (1972), 52-65.
  • 8. A. Hajian, Y. Ito and S. Kakutani, Orbits, sections and induced transformations, Israel J. Math. 18 (1974), 97-115.
  • 9. A. Hajian, Y. Ito and S. Kakutani, Full groups and a theorem of Dye, Advances in Math. 17 (1975), 48-59.
  • 10. A. Hajian and S. Kakutani, Weakly wandering sets and invariant measures, Trans. Amer. Math. Soc. 110 (1964), 136-151.
  • 11. A. Hajian and S. Kakutani, An example of an ergodic m.p.t. defined on an infinite measure space, Proc. on Ergodic Theory, Lecture Notes in Math., vol. 160, Springer-Verlag, Berlin and New York, 1970.
  • 12. T. Hamachi and M. Osikawa, On zero type and positive type transformations with infinite invariant measure, Mem. Fac. Sci. Kyushu University 25 (1971), 280-295.
  • 13. E. Hopf, Theory of measures and invariant integrals, Trans. Amer. Math. Soc. 34 (1932), 373-393.
  • 14. S. Kakutani, Classification of ergodic groups of automorphisms, Proc. on Func. Anal. and Related Topics, Tokyo, April 1969, pp. 392-397.
  • 15. S. Kakutani, A problem in equidistribution, Conference in Measure Theory, Oberwolfach 1975, Lecture Notes in Math., vol. 541, Springer-Verlag, Berlin and New York, 1975.
  • 16. U. Krengel and L. Jones, Transformations without a finite invariant measure, Advances in Math. 12 (1974), 275-295.
  • 17. U. Krengel and L. Sucheston, On mixing in infinite measure spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 150-164.