Lebesgue-Stieljes Measures: Difference between revisions

Revision as of 02:11, 19 December 2020

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

\mu _{F}(A)=\inf \left\{\sum _{i}\mu _{F}(\left[a,b\right])\ :\ A\subset \bigcup _{i}\left[a,b\right]\right\}

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	Given <math> F : R \rightarrow R </math> nondecreasing and right contiuous, define an outer measure by		Given <math> F : R \rightarrow R </math> nondecreasing and right contiuous, define an outer measure by

	:<math>\mu_F(A) = \inf\left\{\sum_i \mu_F(\left[a, b\right]) \ : \ E\subset \bigcup_i \left[a, b\right] \right\}</math>		:<math>\mu_F(A) = \inf\left\{\sum_i \mu_F(\left[a, b\right]) \ : \ A\subset \bigcup_i \left[a, b\right] \right\}</math>