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. By Carathéodory's Theorem, we know that the measure Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double subscripts: use braces to clarify"): {\displaystyle \mu _{F}:=\mu _{F}^{*}\mid _{M}_{\mu }_{F}^{*}} arising from the outer measure Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double subscripts: use braces to clarify"): {\displaystyle \mu _{F}:=\left.\mu _{F}^{*}\right|_{M_{\mu }_{F}^{*}}}