Hostname: page-component-84b7d79bbc-dwq4g Total loading time: 0 Render date: 2024-08-01T20:31:33.798Z Has data issue: false hasContentIssue false
  • English
  • Français

Strongly equivalent invariant measures

Published online by Cambridge University Press:  24 October 2008

J. Rosenblatt
J. Rosenblatt
Affiliation:
Ohio State University, Columbus, Ohio 43210
Get access Rights & Permissions [Opens in a new window]

Abstract

Two measures are strongly equivalent if they have the same sets of zero measure and the same sets of infinite measure. Given a group G of strongly non-singular measurable transformations of a non-atomic positive measure space (X, β, p), if G is amenable, then a necessary and sufficient condition for there to be a G-invariant positive measure on (X, β) which is strongly equivalent to p is that p(E) > 0 implies inf p(gE) > 0 and also p(E) < ∞ implies

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 1 , July 1980 , pp. 33 - 43
Copyright
Copyright © Cambridge Philosophical Society 1980

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)Calderón, A.Sur les mesures invariants. C. R. Acad. Sci., Paris 240 (1955), 1960–1962.Google Scholar
(2)Friedman, N.Introduction to ergodic theory (New York, Van Nostrand, 1970).Google Scholar
(3)Greenleaf, F.Invariant means on topological groups and their applications (New York, Van Nostrand, 1955)Google Scholar
(4)Hajian, A. and Ito, Y.Weakly wandering sets and invariant measures for a group of transformations, J. of Math, and Mech. 18 (1969), 1203–1216.Google Scholar
(5)Millet, A. and Sucheston, L.On the existence of σ-finite invariant measures for operators (preprint, 30 pages).Google Scholar
(6)Rosenblatt, J.Equivalent invariant measures. Israel J. Math. 17 (1974), 261–270.CrossRefGoogle Scholar