Hostname: page-component-7bb8b95d7b-dvmhs Total loading time: 0 Render date: 2024-09-22T11:06:43.792Z Has data issue: false hasContentIssue false
  • English
  • Français

Isomorphic measures on compact groups

Published online by Cambridge University Press:  24 October 2008

S. Grekas
S. Grekas
Affiliation:
S. Grekas, Oitis 12, T.K. 10672 Athens, Greece
Get access Rights & Permissions [Opens in a new window]

Extract

This paper deals with the problem of point realizations of isomorphisms of measure algebras.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 2 , September 1992 , pp. 349 - 360
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Boubbaki, N.. Integration, chapîtres 7, 8 (Hermann, 1963).Google Scholar
[2]Choksi, J. R.. Automorphisms of Baire measures on generalized cubes I and II. Z. Wahrsch. Verw. Gebiete 22 (1972), 195–204CrossRefGoogle Scholar
Choksi, J. R.. Automorphisms of Baire measures on generalized cubes I and II. Z. Wahrsch. Verw. Gebiete 23 (1972), 97–102.CrossRefGoogle Scholar
[3]Choksi, J. R.. Measurable transformations on compact groups. Trans. Amer. Math. Soc. 184 (1973), 101–124.CrossRefGoogle Scholar
[4]Choksi, J. R.. Recent developments arising out of Kakutani's work on completion regularity of measures. In Conference in Modern Analysis and Probability, Contemporary Math. no. 26 (American Mathematical Society, 1984), pp. 81–94.CrossRefGoogle Scholar
[5]Choksi, J. R., Eigen, S. J., Oxtoby, J. S. and Prasad, V. S.. The work of Dorothy Maharam on measure theory. In Ergodic Theory and Category Algebras, Contemporary Math. no. 94 (American Mathematical Society, 1989), pp. 57–71.Google Scholar
[6]Choksi, J. R. and Fremlin, D. H.. Completion regular measures on product spaces. Math. Ann. 241 (1979), 113–128.CrossRefGoogle Scholar
[7]Choksi, J. R. and Prasad, V. S.. Ergodic theory on homogeneous measure algebras. In Measure Theory, Oberwolfach 1981, Lecture notes in Math. vol. 945 (Springer-Verlag, 1982), pp. 366–408.Google Scholar
[8]Choksi, J. R. and Simha, R. R.. Measurable transformations on homogeneous spaces. In Studies in Probability and Ergodic Theory, Adv. in Math. Suppl. Stud. no. 2 (Academic Press, 1978), 269–286.Google Scholar
[9]Fremlin, D. H.. Measure algebras. In Handbook of Boolean Algebra (ed. Monk, J. D.) (North-Holland, 1989).Google Scholar
[10]Graf, S.. Realizing automorphisms of quotients of product σ-fields. Pacific J.Math. 99 (1982), 19–30.CrossRefGoogle Scholar
[11]Halmos, P. R.. Measure Theory (Springer-Verlag, 1974).Google Scholar
[12]Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis, vol. 1 (Springer-Verlag, 1963).Google Scholar
[13]Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis, vol. 2 (Springer-Verlag, 1970).Google Scholar
[14]Johnson, R. A.. Existence of a strong lifting commuting with a compact group of transformations. Pacific J. Math. 76 (1978), 69–81.CrossRefGoogle Scholar
[15]Maharam, D.. Automorphisms of products of measure spaces. Proc. Amer. Math. Soc. 9 (1958), 702–707.CrossRefGoogle Scholar
[16]Maharam, D.. On homogeneous measure algebras. Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 108–111.CrossRefGoogle ScholarPubMed
[17]Maharam, D.. Realizing automorphisms of category algebras. Topology Appl. 10 (1979), 161–174.CrossRefGoogle Scholar
[18]Montgomery, D. and Zippin, L.. Topological Transformation Groups (Interscience, 1955).Google Scholar
[19], A. and Tulcea, C. Ionescu. On the existence of a lifting commuting with the left translations of an arbitrary locally compact group. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 2, part 1, pp. 63–97.Google Scholar
[20]von Neumann, J.. Einige Sätze über die messbare Abbildungen. Ann. of Math. (2) 33 (1932), 574–586.CrossRefGoogle Scholar
[21]Weil, A.. L'intégration dans les groupes topologigues et ses applications, 2nd edition (Hermann, 1951).Google Scholar