Let \(m_*\) be the outer measure on \(\RR^n\). A set \(E\subseteq \RR^n\) is measurable if for every \(\varepsilon>0\) there exists an open set \(G \supseteq E\) with \(m_*(G\setminus E)<\varepsilon\).
When is a set $E \subseteq \RR^n$ measurable?
Lebesgue measurability of a set
FD-D4S7E