Lebesgue-Stieljes Measures: Difference between revisions

Revision as of 02:07, 19 December 2020

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) \ : \ E\subset \bigcup_i I_i \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~~(b_i) \ : \ E\subset \bigcup_i I_i \right\}</math>		:<math>\mu_F(A) = \inf\left\{\sum_i \F(b_i) \ : \ E\subset \bigcup_i I_i \right\}</math>