Geodesic
Large Sets not Containing Images of a Given Sequence
Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 41-43

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DOI

In the first part we construct a subset H of positive measure in the unit interval and a zero-sequence {an} so that H contains no homothetic copy of {an}. In Theorem 2 we prove that if ε > 0 and a zero-sequence {an} are given then there exists a set A of measure less than ε so that covers the interval. An application of this result is Theorem 3: for any sequence {an} and ε > 0 there is a set H of measure 1 - ε such that for no N and c is {an + c}n ≥ N contained by H.
DOI : 10.4153/CMB-1983-007-7
Mots-clés : primary: 28A05, secondary: 54G20, 51M25, real sequences, measurable sets 
Komjáth, Péter. Large Sets not Containing Images of a Given Sequence. Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 41-43. doi: 10.4153/CMB-1983-007-7
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     title = {Large {Sets} not {Containing} {Images} of a {Given} {Sequence}},
     journal = {Canadian mathematical bulletin},
     pages = {41--43},
     year = {1983},
     volume = {26},
     number = {1},
     doi = {10.4153/CMB-1983-007-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-007-7/}
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