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Covering Finite Sets by Ergodic Images

Published online by Cambridge University Press:  20 November 2018

J. Michael Steele
J. Michael Steele*
Affiliation:
Department of Mathematics, University of British Colombia, 2075, Westbrook Place Vancouver, B.C., V6T 1W5
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Abstract

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For any ergodic transformation T a set A of measure less than ∈ is constructed with the property that for every finite set F there is a j = j(F) such that F ⊂ T-iA. The basic tool used to prove this is a purely combinatorial result which says there is a small subset of { l, 2, …, n } which can be shifted a small amount to cover any k set in {j: δn ≤j≤n}. Applications are given to the theory of combinatorial entropy.

Keywords

Ergodicaperiodicentropycombinatorial method
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 1 , 01 March 1978 , pp. 85 - 91
Copyright
Copyright © Canadian Mathematical Society 1978

References

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