Some generalizations of the ergodic theorem
- 1 July 1942
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 38 (4) , 325-343
- https://doi.org/10.1017/s0305004100022027
Abstract
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 thatKeywords
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