TITLE: Does a set with strictly positive Lebesgue measure contain an interval?
QUESTION [11 upvotes]: I am studying a function whose Fourier transform is zero on a set of strictly positive Lebesgue measure and I need to know this:
If a set has a strictly positive Lebesgue measure can we prove that it contains an interval?
Help is much appreciated

REPLY [18 votes]: The irrationals are an easy example of not having this property.