Lebesgue-Stieljes Measures

Given $F:R\rightarrow R$ nondecreasing and right contiuous, define an outer measure by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_F(A) = \inf\left\{\sum_i \(F(b_i) - F(a_i)) \ : \ A\subset \bigcup_i \left[a_i, b_i\right] \right\}}