Lebesgue null set
= Lebesgue null set
{c}
{title2=$\lambda(E)=0$}
A Lebesgue null set has zero <Lebesgue measure>. Since <Lebesgue measure> is complete, every <subset> of one is also measurable and null. The <Cantor set> is an <uncountable> example with positive <Hausdorff dimension>; the <rational numbers> form a <countable>, <dense> example with <Hausdorff dimension> zero. Being null does not imply being empty or having finitely many points.