Q: Construct an open subset E of [0,1] having Lebesgue measure [itex]m(E)=\epsilon[/itex] such that [itex]0<\epsilon<1[/itex] which is dense [0,1].(adsbygoogle = window.adsbygoogle || []).push({});

A: The fat Cantor set. I need help proving it is dense in [0,1]. The usual Ternary expansion arguement stuff won't work as the sets used are of length [tex]\frac{\epsilon}{3^k}[/tex] at the k^{th}iteration. Ideas?

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# Construct an open subset of [0,1] of arbitrary measure dense therein

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