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Strongly equivalent invariant measures

Published online by Cambridge University Press:  24 October 2008

J. Rosenblatt
J. Rosenblatt
Affiliation:
Ohio State University, Columbus, Ohio 43210
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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

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References

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