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Covering Finite Sets by Ergodic Images
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 1978
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