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) \ : \ E\subset \bigcup_i I_i \right\}}