= Lebesgue measurable set
{c}
= Lebesgue measurable
{c}
{synonym}
A <subset> $E\subseteq\mathbb R$ is a <Lebesgue measurable set> when it satisfies <Carathéodory's criterion> for <Lebesgue outer measure>: for every <subset> $A\subseteq\mathbb R$,
$$
m^*(A)=m^*(A\cap E)+m^*(A\setminus E).
$$
These sets form the <Lebesgue sigma-algebra>, the completion of the <Borel sigma-algebra> with respect to <Lebesgue measure>. Equivalently, $E$ differs from a <Borel set> by a <subset> of a <Borel null set>.
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