Given F : R → R {\displaystyle F:R\rightarrow R} nondecreasing and right contiuous, define an outer measure by
where μ F ∗ ( ( a , b ] ) = F ( b ) − F ( a ) {\displaystyle \mu _{F}^{*}(\left(a,b\right])=F(b)-F(a)}
nondecreasing and right contiuous, define an outer measure by
![{\displaystyle \mu _{F}^{*}(A)=\inf \left\{\sum _{i}\mu _{F}^{*}(\left(a,b\right])\ :\ A\subset \bigcup _{i}\left(a,b\right]\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/426f2df40dd3f9b86da35165f7a52ba887196cfc)
![{\displaystyle \mu _{F}^{*}(\left(a,b\right])=F(b)-F(a)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf603aad0fe2f4fd3be8821bbbd477146bb759c)