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Assume that a sequence (fn)n of integrable functions converges strongly to an integrable limit f. Prove that (1) (fm)n converges to f in mean, (2) (fn)n converges to f absolutely in mean,

Assume that a sequence (fn)n of integrable functions converges strongly to an integrable limit f. Prove that (1) (fm)n converges to f in mean, (2) (fn)n converges to f absolutely in mean,

Advanced Engineering Mathematics
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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Question 1 Assume that a sequence (fn)n of integrable functions converges strongly to an integrable limit f. Prove that (1) (fn)n converges to f in mean, (2) (fn)n converges to f absolutely in mean,
Transcribed Image Text:Question 1 Assume that a sequence (fn)n of integrable functions converges strongly to an integrable limit f. Prove that (1) (fn)n converges to f in mean, (2) (fn)n converges to f absolutely in mean,
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