Lebesgue-Stieljes Measures
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Given nondecreasing and right contiuous, define an outer measure by
where and the infimum taken over all coverings of A by countably many semiopen intervals.
Given 
![{\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)
where ![{\displaystyle \mu _{F}^{*}(\left(a,b\right])=F(b)-F(a)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf603aad0fe2f4fd3be8821bbbd477146bb759c)