$\textbf{Outer measure}$
Let $X$ be a set and let $\mathscr{P}(X)$ be the collection of all subsets of $X$. An outer measure on $X$ is a function $\mu^*:\mathscr{P}(X)\to[0,\infty]$ such that
1) Null empty set: $\mu^*(\varnothing)=0$
2) Monotonicity: $A\subseteq B\subseteq X\implies\mu^*(A)\leq\mu^*(B)$
3) Countable subadditivity: $\{A_i\}$ is an infinite sequence of subsets of $X$ $\implies$ $\mu^* (\cup_{i=1}^\infty A_i)\leq\sum_{i=1}^\infty \mu^*(A_i)$
$\textbf{Outer measure}$
Let $X$ be a set and let $\mathscr{P}(X)$ be the collection of all subsets of $X$. An outer measure on $X$ is a function $\mu^*:\mathscr{P}(X)\to[0,\infty]$ such that
1) Null empty set: $\mu^*(\varnothing)=0$
2) Monotonicity: $A\subseteq B\subseteq X\implies\mu^*(A)\leq\mu^*(B)$
3) Countable subadditivity: $\{A_i\}$ is an infinite sequence of subsets of $X$ $\implies$ $\mu^* (\cup_{i=1}^\infty A_i)\leq\sum_{i=1}^\infty \mu^*(A_i)$
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๐๐ฎ๐ญ๐๐ซย ๐ฆ๐๐๐ฌ๐ฎ๐ซ๐
Let ๐ be a set and let ๐ซ(๐) be the collection of all subsets of ๐. An outer measure on ๐ is a function ๐*:๐ซ(๐)โ[0,โ] such that
1) Null empty set: ๐*(โ )=0
2) Monotonicity: ๐ดโ๐ตโ๐ โน ๐*(๐ด)โค๐*(๐ต)
3) Countable subadditivity: {๐ดแตข} is an infinite sequence of subsets of ๐ โน ๐*(โชแตขโโโแชฒ ๐ดแตข)โคโแตขโโโแชฒ ๐*(๐ดแตข)