Lebesgue-Stieljes Measures: Difference between revisions
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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 \F(b_i) - F(a_i) \ : \ A\subset \bigcup_i \left[ | :<math>\mu_F(A) = \inf\left\{\sum_i \F(b_i) - F(a_i) \ : \ A\subset \bigcup_i \left[a_i, b_i\right] \right\}</math> | ||
Revision as of 02:02, 19 December 2020
Given 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) - F(a_i) \ : \ A\subset \bigcup_i \left[a_i, b_i\right] \right\}}