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Return times and conjugates of an antiperiodic transformation

Published online by Cambridge University Press:  19 September 2008

Steve Alpern
Steve Alpern*
Affiliation:
From the Department of Mathematics, London School of Economics, England
*
†Address for correspondence: Dr Steve Alpern, Department of Mathematics, London School of Economics, Houghton Street, London, England.
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Abstract

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Denote by G the group of all μ-preserving bijections of a Lebesgue probability space (X, Σ, μ) and by C the conjugacy class of an antiperiodic transformation σ in G. We present several new results concerning the denseness of C in G with respect to various topologies. One of these asserts that given any weakly mixing transformation τ in G and any F with μ(F) < 1, there is a transformation in C which agrees with τ a.e. on F.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 2 , June 1981 , pp. 135 - 143
Copyright
Copyright © Cambridge University Press 1981

References

REFERENCES

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