Math 321 - Riemann–Stieltjes Integrals

Or 3 there is a 1 j n with xi1 sj in this case xi

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Unformatted text preview: ] (either [a, s1 ), or (sj −1 , sj ) for some 2 ≤ j ≤ n, or (sn , b]) on which α is required to be constant. In this case α(xi ) − α(xi−1 ) = 0. or (2) there is a 1 ≤ j ≤ n with xi = sj . In this case α(xi ) − α(xi−1 ) = α(sj ) − α(sj −). or (3) there is a 1 ≤ j ≤ n with xi−1 = sj . In this case α(xi ) − α(xi−1 ) = α(sj +) − α(sj ). These three possibilities are illustrated below, with the points of P indicated by hash marks. (1) (2) (3) (1) (2) (3) (2) (3) (1) a January 9, 2008 s1...
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