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Twofold mixing implies threefold mixing for rank one transformations

Published online by Cambridge University Press:  19 September 2008

Steven Arthur Kalikow
Steven Arthur Kalikow
Affiliation:
Mathematics Department, Stanford University, Stanford CA 94305, USA
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Abstract

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This paper addresses the following long-standing open question: If a stationary transformation on a probability space obeys the property

for all measurable sets A1, A2, does it follow that

for all measurable sets A1, A2, A3? Here we answer the question affirmatively for a certain class of transformations.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 2 , June 1984 , pp. 237 - 259
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Halmos, P. R.. Lectures on Ergodic Theory. Chelsea Publishing Co: New York, (1956).Google Scholar
[2]Rohlin, V. A.. On endomorphisms of compact commutative groups. Izv. Acad. Nauk. SSSR, 13 (1949), 329–340. (In Russian.)Google Scholar