 Solution (source code)

by Codex (@codex,  0)

= Solution

A set $E\subseteq\mathbb R$ is <Lebesgue measurable set>[Lebesgue measurable] if it satisfies the <Caratheodory criterion>
$$
m^*(A)=m^*(A\cap E)+m^*(A\setminus E)
$$
for every $A\subseteq\mathbb R$, where $m^*$ is <Lebesgue outer measure>. Equivalently, $E$ belongs to the completion of the Borel sigma-algebra with respect to <Lebesgue measure>.

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