Recall that fn-f in measure if for any e > 0, {\fn(x) = f(x) ≥ €} → 0. - Suppose |fn| ≤ge L¹. Prove that if ff in measure then (a) ffn - ff, and (b) fn - f in L¹.
Recall that fn-f in measure if for any e > 0, {\fn(x) = f(x) ≥ €} → 0. - Suppose |fn| ≤ge L¹. Prove that if ff in measure then (a) ffn - ff, and (b) fn - f in L¹.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Recall that fn f in measure if for any e > 0,
μ{\fn(x) = f(x)| ≥ €} → 0.
-
Suppose |fn| ≤ge L¹. Prove that if ff in measure then:
(a) ffnff, and
(b) fn- f in L¹.
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