$\textbf{Measurable with respect to an outer measure}$
Let $X$ be a set and $\mu^*$ an outer measure on $X$. A subset $B$ of $X$ is $\mu^*$-measurable (or measurable with respect to $\mu^*$) if for every subset $A$ of $X$ $$\mu^*(A)=\mu^*(A\cap B)+\mu^*(A\cap B^\complement) $$
$\textbf{Measurable with respect to an outer measure}$
Let $X$ be a set and $\mu^*$ an outer measure on $X$. A subset $B$ of $X$ is $\mu^*$-measurable (or measurable with respect to $\mu^*$) if for every subset $A$ of $X$ $$\mu^*(A)=\mu^*(A\cap B)+\mu^*(A\cap B^\complement) $$
copied
๐๐๐๐ฌ๐ฎ๐ซ๐๐๐ฅ๐ย ๐ฐ๐ข๐ญ๐กย ๐ซ๐๐ฌ๐ฉ๐๐๐ญย ๐ญ๐จย ๐๐งย ๐จ๐ฎ๐ญ๐๐ซย ๐ฆ๐๐๐ฌ๐ฎ๐ซ๐
Let ๐ be a set and ๐* an outer measure on ๐. A subset ๐ต of ๐ is ๐*-measurable (or measurable with respect to ๐*) if for every subset ๐ด of ๐
๐*(๐ด)=๐*(๐ดโฉ๐ต)+๐*(๐ดโฉ๐ตแถ)