Geodesic
Translates of Sequences in Sets of Positive Measure
Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 497-498

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Given a measurable set A of real numbers with measure mA > 0, and a sequence {dn } of real numbers converging to zero, is there always an x such that x + dn ∈ A for all n sufficiently large?The answer to this question, which was posed to the authors by P. Erdös, is NO. 
Borwein, D.; Ditor, S. Z. Translates of Sequences in Sets of Positive Measure. Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 497-498. doi: 10.4153/CMB-1978-084-5
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     title = {Translates of {Sequences} in {Sets} of {Positive} {Measure}},
     journal = {Canadian mathematical bulletin},
     pages = {497--498},
     year = {1978},
     volume = {21},
     number = {4},
     doi = {10.4153/CMB-1978-084-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-084-5/}
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