I have ran across this in the hypothesis of one certain theorem.
Let $X$ be a separable metric space with a Borel regular outer measure $\mu^{*}$ such that $\mu^{*}X = 1 $.
I don't understand the essence of this. what does it mean that a separable metric space is endowed with a boreal regular outer measure $\mu^{*}$ such that $\mu^{*}X = 1 $ ?
How is metric defined there?
Any help would be appreciated.