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[Manual] Daniel W. Stroock - Instructor`s Solutions Manual to Essentials of Integration Theory for Analysis-S

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[Manual] Daniel W. Stroock - Instructor`s Solutions Manual to Essentials of Integration Theory for Analysis-S




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Solutions Manual

§ 1.1 (1.1.10): First note that, for any α ∈ R, αf is Riemann integrable if f is. To prove that f ∨ g is Riemann integrable if f and g are, observe that a ∨b a∨b ≤ |a a|∨|b b| ≤ |a a|+|b b| for any a, a , b, and b ∈ R. Thus, for any C, U f ∨ g; C L f ∨ g; C ≤ U(f ; C) L(f ; C) + U(g; C) L(g; C) . Now apply the nal part of Lem…(skip)
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