Measurable set
= Measurable set
{title2=$A\in\mathcal F$}
A <subset> of $X$ is measurable relative to a <sigma-algebra> $\mathcal F$ when it belongs to $\mathcal F$. A <measure> defined on $\mathcal F$ assigns sizes to these sets. Measurability depends on the chosen <sigma-algebra>; for example, a <Lebesgue measurable set> need not be a <Borel set>.