(3) Prove that if a sequence (fn)n converges to f in measure, then the limit fis unique, almost everywhere.(Hint: first show that for every & > 0,{\f − g\ > €} = {\ƒ - fn] > } U {19 - fnl > > {})(4) Prove that if a sequence (fn)n converges to f in measure, then the sequence(Ifn)n converges to [f] in measure, too.

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Answered: (3) Prove that if a sequence (fn)n…

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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(3) Prove that if a sequence (fn)n converges to f in measure, then the limit f is unique, almost everywhere. (IT: 11