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Catching and Missing Finite Sets

Published online by Cambridge University Press:  20 November 2018

Martin H. Ellis
Martin H. Ellis*
Affiliation:
Department of Mathematics, State University of New York, Albany, N.Y. 12222
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Abstract

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IfT is a 1-1 bimeasurable measure-preserving aperiodic transformation on a probability space X which is a Lebesgue space, then {A:A⊂X and for almost every pair of finite sets F and G there is an n∈N satisfying F⊂TnA and G ∩ TnA=ϕ} is dense in the σ-algebra of measurable sets.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 4 , 01 December 1978 , pp. 419 - 425
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Halmos, P. R., Lectures on ergodic theory, Chelsea, New York, 1956.Google Scholar
2. Jones, L. K. and Krengel, U., On transformations without finite invariant measure, Advances in Mathematics 12 (1974), 275-295.Google Scholar
3. Steele, J. M., Covering finite sets by ergodic images, Canadian Mathematical Bulletin, Vol. 21, (1978), 85-92.Google Scholar