Lebesgue-Stieljes Measures: Difference between revisions

Revision as of 02:17, 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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	:<math>\mu_F(A) = \inf\left\{\sum_i \mu_F(\left(a, b\right]) \ : \ A\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>

	where {{math\|''~~μ<sub>F</sub>~~''}}		where {{math\|''w''([''s'',''t'')) {{=}} ''g''(''t'') − ''g''(''s'')}}