Lebesgue-Stieljes Measures

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

Failed to parse (unknown function "\F"): {\displaystyle \mu_F(A) = \inf\left\{\sum_i \F(b_i) - F(a_i) \ : \ A\subset \bigcup_i {{math|[''a_i'', ''b_i'']}} \right\}}