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Oct 13, 2020 at 7:28 comment added Duplicate You probably get it wrong. Given the set $E$ I am asking whether there is $l>0$(obviously depending on $E$) such that the above intersection is non-empty or not. For example if your $E=(0,1)$ then if we take $l=0.001$ then the above intersection will be non-empty.
Oct 7, 2020 at 21:27 comment added David Handelman There is possibly something wrong with the formulation of this question. First, you might as well assume that $l=1$. Second, if $E $ is the any proper subset of the open interval $(0,1)$, then the intersection is going to be empty. Perhaps you mean $E$ is a subset of full measure (that is, its complement has measure zero)?
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Oct 7, 2020 at 5:33 vote accept Duplicate
Oct 7, 2020 at 5:16 answer added Martin Väth timeline score: 7
Oct 7, 2020 at 4:39 history asked Duplicate CC BY-SA 4.0