5. Suppose that IN : [-71, 71] ~ R are integrable and IN ~ I uniformly on...

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5. Suppose that IN : [-71", 71"] ~ R are integrable and IN ~ I uniformly on [-71",71"] as N ~ 00.

(a) Prove that ak(fN) ~ ak

(f) and bk(fN) ~ bk(f), as N ~ 00, uniformly in k.

(b) Show that part

(a) holds under the weaker hypothesis J~oo [: I/(x) - IN(X)I dx = O.

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An Introduction To Analysis

ISBN: 9780131453333

3rd Edition

Authors: William R. Wade

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Question Posted: Jul 19, 2024 01:08 AM

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5. Suppose that IN : [-71, 71] ~ R are integrable and IN ~ I uniformly on...

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An Introduction To Analysis

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