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Some generalizations of the ergodic theorem

Published online by Cambridge University Press:  24 October 2008

H. R. Pitt
H. R. Pitt
Affiliation:
King's CollegeAberdeen
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Extract

Throughout this paper we shall suppose that denotes a set of elements x in which a Lebesgue measure is defined and that itself is measurable and has finite measure. A (1, 1) transformation T of into itself is called an equimeasure transformation if the transform T E of any measurable subset E of is measurable and has measure equal to that of E. Then, if f(x) is integrable in , it is plain that f(Tx) is also integrable and that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 4 , November 1942 , pp. 325 - 343
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

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