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