let $\displaystyle 0<\epsilon<1$, construct a open set E contained in [0,1] such that E is dense in [0,1], and $\displaystyle m(E)=\epsilon$. $\displaystyle m$ is the lebesgue measure in real line.)

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- Jan 6th 2010, 07:39 AMShanksSet Construction
let $\displaystyle 0<\epsilon<1$, construct a open set E contained in [0,1] such that E is dense in [0,1], and $\displaystyle m(E)=\epsilon$. $\displaystyle m$ is the lebesgue measure in real line.)