Does $m(E)>0$ imply that $E$ must contain a nondegenerate interval?
$E\subset\mathbb{R}.$ $m$ refers to Lebesgue measure. $I$ refers to a nondegenerate interval.
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1$\begingroup$ No. Interestingly enough, though, if $m(A)>0$ then $(-a,a) \subseteq A-A$ for some $a> 0$. Where $A-A$ is the difference set of $A$. $\endgroup$– doppzCommented Oct 26, 2013 at 21:20
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2 Answers
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For a simple counterexample, try the irrational numbers in any interval
