# Thread: lebesgue measurable set construction

1. ## lebesgue measurable set construction

Construct a lebesgue measurable set $S$ such that for any nonempty interval $I, 0< m(S\cap I)< m(I)$,
where $m$ is the lebesgue measure in real line.
Is it possible that S has finite lebesgue measure?

2. .>-<. Any1 help me please.
Open to any solution or idea.