Math 321 - Riemann–Stieltjes Integrals

Now let p a x0 x1 xp b p be any partitition

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Unformatted text preview: (2) the norm or mesh of Pε = Pε = max xi − xi−1 < δ with 1≤i≤m δ = min |s2 − s1 |, · · · , |sn − sn−1 |, δ0 and δ0 is given by Insert (∗) here. Now let P = {a = x0 , x1 , · · · , xp = b} ⊃ Pε be any partitition finer than Pε and T = {t1 , · · · , tp } be any choice for P and consider each term in p S (P, T, f, α) = f (ti ) α(xi ) − α(xi−1 ) i=1 For each 1 ≤ i ≤ p, either (1) neither xi nor xi−1 is in {s1 , · · · , sn }, in which case both xi and xi−1 lie in a subinterval of [a, b...
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