Geodesic
Covering Finite Sets by Ergodic Images
Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 85-91

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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.
DOI : 10.4153/CMB-1978-013-3
Mots-clés : Ergodic, aperiodic, entropy, combinatorial method 
Steele, J. Michael. Covering Finite Sets by Ergodic Images. Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 85-91. doi: 10.4153/CMB-1978-013-3
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     author = {Steele, J. Michael},
     title = {Covering {Finite} {Sets} by {Ergodic} {Images}},
     journal = {Canadian mathematical bulletin},
     pages = {85--91},
     year = {1978},
     volume = {21},
     number = {1},
     doi = {10.4153/CMB-1978-013-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-013-3/}
}
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