Complete measure

In mathematics, a complete measure (or, more precisely, a complete measure space) is a measure space in which every subset of every null set is measurable (having measure zero). More formally, a measure space (X, Σ, μ) is complete if and only if

${\displaystyle S\subseteq N\in \Sigma {\mbox{ and }}\mu (N)=0\ \Rightarrow \ S\in \Sigma .}$