# Does every Borel set with a positive Lebesgue measure contain a closed interval $[a,b]$ with $a<b$?

The question is simple:

Does every Borel set with a positive Lebesgue measure contain a closed interval $[a,b]$ with $a<b$?

If not than I need a counterexample; if so some kind of proof would be nice. I have no idea how to get closed intervals into a Borel set.

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